Mercedes lost both of its protests after Lewis Hamilton lost the F1 world title to Verstappen on the final lap of the last race at the season-ending Abu Dhabi Grand Prix.
After losing the protests, Mercedes confirmed it has lodged an intention to appeal the verdict relating to the second protest about the safety car protocol.
The intention to appeal means Mercedes have 96 hours to decide if they will launch a full appeal, so it could be days before an official conclusion is reached.
Verstappen overtook Hamilton on lap 58 in thrilling style after a crash involving Nicholas Latifi brought out the safety car with just a few laps left and confusion surrounded the restart.
One of the lost protests was whether Verstappen had broken rules by passing Hamilton before the safety car period had ended, when they were jostling next to each other waiting for the restart.
"Although Car 33 (Verstappen) did at one stage, for a very short period of time, move slightly in front of Car 44 (Hamilton), at a time when both cars were accelerating and braking, it moved back behind Car 44," stewards concluded. "It was not in front when the Safety Car period ended (i.e. at the line). Accordingly, the Protest is dismissed."
The other protest concerned the restart procedure itself and the number of lapped cars overtaking the safety car, having been given the green light to do so.
Of the lapped drivers, only Lando Norris, Fernando Alonso, Esteban Ocon, Charles Leclerc and Sebastian Vettel overtook — those five were originally between Hamilton and Verstappen — while Daniel Ricciardo, Lance Stroll and Mick Schumacher did not.
Mercedes argued Hamilton would have won the race if all had overtaken the safety car due to the time required, making a final lap showdown impossible. Stewards ruled that it made no difference since the other three were not interfering with the outcome of the race, and also that race director Michael Masi had authority "to control the use of the safety car" in this case.
Before Latifi's crash, Hamilton was coasting to world title number eight.
There had already been one virtual safety car deployed earlier in the race for a smaller crash, but this time the real one came out with little time left to remove Latifi's car and clear debris off the track.
Verstappen's Red Bull team decided to pit him to switch to new tires while Mercedes stayed out to keep track position. But it ultimately left Hamilton at Verstappen's mercy on far quicker, fresh tires than Hamilton's fading, slower ones. They were supposed to take him over the line, but in the end they couldn't hold off Verstappen.
Initially, the decision was taken not to let lapped cars overtake the safety car, which would have meant several drivers would have been in Verstappen's way at the restart and made it more difficult to reach Hamilton over one lap.
Red Bull team principal Christian Horner was in radio contact with Masi at that point and said "(but) we only need one lap" to finish a race properly.
Masi then reversed the call to allow lapped cars to pass and set up that final lap of racing.
"When everything is clear you have to release the track, so that's a fair point from the race direction," Verstappen said after the race in agreement.
Verstappen made his pass in the fifth turn and Hamilton had one last shot. He pulled his Mercedes even with the Red Bull but couldn't clear it. Verstappen became the first Dutch world champion and thwarted Hamilton's bid to move one clear of Michael Schumacher as the most successful driver in F1 history.
The finish angered Mercedes boss Toto Wolff, who demanded "the last lap be reinstated."
But Masi was firm in his reply.
"Toto, it's called a motor race," he said. "We want car racing."
The other protest was for the way Verstappen drove before the race restarted. He pulled right alongside Hamilton near the end of lap 57 and fractionally ahead on lap 58.
The regulations say "no driver may overtake another car on the track, including the safety car, until he passes the line for the first time after the safety car has returned to the pits."
Mercedes had lodged their protests within the allotted 30-minute window after the race.
The team said it would "not make any further comment on the detail of that until the hearing has been conducted".
Horner said "we are disappointed there has been a protest, but we trust in the FIA".
Verstappen was also asked to comment on Mercedes's decision to protest.
"Not much really to say about that, it also sums up a little bit the season," said Verstappen, who in previous races has expressed frustration at some penalties that have been given against him — including two in the last race in Saudi Arabia.
He had responded with sarcasm to the initial decision not to allow lapped cars to overtake the safety car.
"Of course, I'm not surprised," Verstappen said with an air of resignation.
Minutes later, he was overtaking Hamilton on the way to glory.
'Credibility of the sport has been brought into question'
After Mercedes' second protest was rejected, BBC F1 journalist Andrew Benson said he believes there could be more drama to come.
"I suspect this hasn't ended here," Benson said. "The second protest by Mercedes has been rejected, I don't think Mercedes are going to be happy about that.
"Lots of people up and down the pitlane have got questions about how the FIA have handled this race.
"I have spoken to people who think if it had not been a world championship decider it probably would have ended behind a safety car.
"Was the way things were dealt with by FIA race director Michael Masi appropriate?
"All these issues need to be discussed.
"The creditability of the sport has been brought into question this weekend and I think a lot of people will have serious questions about what has happened."
I think the FIA made the right call in race time. Nobody wanted to see the finale end with the drivers following the safety car. What we got was far more exciting.
this is what happens when a sport decides to turn itself into scripted entertainment. rules stop being rules. the only guiding principle is what sells the product
Red Bull team principal Christian Horner told BBC Radio 5 after the protests were dismissed: "They have done an amazing job this year, showing passion and determination.
"Max got a little bit lucky with the safety car tonight but still had to come through with the strategy.
"We didn't want it to end in the steward's room. They have come to the right decision, we are grateful.
"Michael Masi wanted to let them race. That's what we have talked about for years. Nikki Lauda came up with the concept of 'let them race' and that's what they did.
"Max is a very worthy world champion and we are very proud of him."
Verstappen, on the other hand, was looking forward to a drink after a "stressful" day.
"Very. It has been a very stressful day. [I'm going to] have a tiny drink," he told Sky Sports.