"I really didn't think he was going to pull that off," Horner told Sky Sports F1.
"Lewis with eight-lap newer tyres, and the first set of hards that came off, we were pretty much down to the canvas. And then thinking, well, we're not going to have much left at the end here."
"But I think really, the way he [Max] managed that tyre through the last stint to make sure he had enough left for the last five or six laps. With Lewis, you know the end of the race he's going to be so strong. He's gone long, he's bought himself an advantage.
"To lose a race like that in the last two or three laps, we lost one to Mercedes in Bahrain and that really hurt. So to lose one here would have really painful. Max just held on, he did a great job. He drove a great race, really smartly, and had just enough at the end there."
Although there were battles going on through the field, especially between the Ferraris and the McLarens, the focus of the 140,000 fans jam-packed into the circuit, most not wearing masks or social distancing despite Texas alone having 123,000 active Covid-19 cases and recording over 70,000 deaths, was on the Verstappen-versus-Hamilton championship battle.
And it didn't disappoint, although Hamilton and team boss Toto Wolff couldn't disguise their disappointment at the outcome. After all, Hamilton has won the race five times, whereas prior to Sunday's (Monday NZT) victory, Verstappen's best result was second in 2018.
Red Bull had hoped Sergio Perez, starting third on the grid, may have been able to help Verstappen by staying out a little longer to try to undercut Hamilton, but as it transpired, the pace of the two championship contenders effectively eliminated anyone else influencing the outcome.
Although on the last lap, as Hamilton closed in on Verstappen, the latter was desperate to get around the lapped Haas of Mick Schumacher, as he explained to Sky Sports.
"It was tough ... the tyres were not in a great state and I know how much Lewis was catching," Verstappen said.
"But we managed to hold on at the end. It is quite difficult to pass around here but, of course, when your tyres are going you can lose a lot of lap time.
"Luckily it was just enough. Also, with two laps to go, I could see the Haas car in front of me and I was like, 'Oh. Please move out of the way!' But it was his right, I was only within 1.5 seconds because my tyres were starting to fall away and so when you are following it makes it more difficult. Luckily he ended up giving me the DRS, which helped a little bit."
On the pit wall, the legs of Horner, which twitch at the best of times, were going into overdrive as his main man approached Schumacher's car.
"Mick on the last lap cost us, but he also gave us DRS - he nearly gave me a heart attack as well," Horner explained.
"But Max just managed to keep enough in hand and that was a classy, classy drive, a crucial drive. I think I've aged about 25 years in that race. I really didn't think we could hang on at the end there because it was such a long stint and we were out of tyres after I last spoke to you - I didn't want to give that away," Horner told Sky Sports.
For Hamilton, it was a case of giving it all he had, which on the day wasn't enough.
"We gave it everything we had and they [Red Bull] were just quicker than us this weekend," he said. "It looked like they just had better rear end and a little less bit sliding than we had. I had a great start, I gave it absolutely everything today and it was just unfortunate I couldn't convert it at the end. They just had the upper hand this weekend and we couldn't really have asked for more."
Toto Wolff said the problem was the Mercedes was too slow on the medium tyres.
"I think we started really well on Friday, and then went a little bit off track, and we recovered in the race," he said. "For us, P2 was, for me personally, better than I expected. At the end, it's always a fine line between downforce and drag."
"I thought it was some interesting strategy games and great racing," he added.
"But at the end, we thought we had a sniff at it, but it wasn't enough. They went for a super-aggressive first stop, and that was bold. We did that in Bahrain at the beginning of the year and we won, and then they covered it the second time and we thought maybe that's enough at the end to get them, but they deserved to win today."
Given there has been at times some not-so-friendly and quite-personal acrimonious banter between him and Horner, an acknowledgment that Red Bull deserved the win will restore some balance to the team's respect for one another in what is an increasingly intense battle for both the drivers' and constructors' championships.
With Perez finishing third after a spirited drive in the heat despite not feeling well and his drink bottle malfunctioning, and with Valtteri Bottas finishing only sixth after taking yet another grid penalty for an engine change, Red Bull is only 23 points behind Mercedes in the Constructors' race.
Charles Leclerc finished fourth for Ferrari, holding off an initial challenge from Daniel Ricciardo in the McLaren.
Bottas, Carlos Sainz in the second Ferrari and Lando Norris in the other McLaren, were next.
The battle between McLaren and Ferrari for third place in the constructor's title seems set to continue until season end, with just 3.5 points separating them. Further down the grid, there will be a concern at Alpine as both cars failed to finish with rear-end issues.
In recent weeks, Hamilton has been resorting to mind games with Verstappen, indicating he was not stressed about the championship battle.
Had he won the US race for a seventh time, and with the extra point gained for fastest lap, he would be leading the championship yet again by two points. Instead, he is now 12 points behind, which, although only a small margin, it at least forces Hamilton and Mercedes to play catch-up, which was something they failed to do, albeit narrowly, in Austin.
Hamilton may say publicly he is not feeling any pressure as a seven-time champion, but he knows an eighth title will lift him above Michael Schumacher in that respect, and give credence to being able to claim he is the GOAT, the greatest of all time.
He is also aware the vast regulation changes next year, with a revolutionary design for the cars aimed at creating a more even playing field, together with budget caps, will probably take away the dominance Mercedes has had since the start of the new turbo-hybrid engine era in 2014.
Also, Hamilton is now 36, whereas Verstappen is only 24, so it can only get harder for Hamilton to maintain his incredible consistency and ability to win races.
Verstappen, on the other hand, is desperate to win his first championship. Any driver who has won 18 grand prix would expect to have won a championship or more with such a winning total.
The late great Sir Stirling Moss, with 16 wins, is considered the best grand prix driver not to have won a world title, a mantle Verstappen won't be keen to have taken over, so there is pressure on him to become world champion.
His drive in Austin suggests he's more than capable of handling whatever Hamilton may throw at him, on and off the track, and the good news is that both avoided any contact in this latest epic encounter, and their duel is set to continue in Mexico in two weeks.