"I lost. Sad today for that, obviously," said Nadal, who was also runner-up at Wimbledon in 2006, 2007 and 2011.
"But end of the day, that's sport. Good moments, bad moments. Obviously today is a bad moment for me. I just need to accept these kinds of things can happen.
"I am a good loser but I will keep going. It's not the end. Life continues, my career, too."
For Brown, who once drove to tournaments in a camper van to save money, it was his second win against Nadal, having beaten him on grass at Halle in 2014.
He also took another former champion, Lleyton Hewitt, in 2013, but had never been beyond round three.
"I had actually never been on Centre Court before," said the 30-year-old.
"They asked me before the match if I wanted to go on the court.
"I didn't know what was going to happen, so I just said I'll just go on when I play.
"I thought it might freak me out a little bit but, I don't know if it was the match in Halle, it felt very familiar."
Brown will next face Serbia's Viktor Troicki.
There were no such problems for former champions Roger Federer and Andy Murray, who swept into the third round.
Seven-time winner and second seed Federer eased to a 6-4, 6-2, 6-2 victory over American Sam Querrey, the world No 36.
The Swiss fired 32 winners and hit just nine unforced errors in an 86-minute stroll and will face Australian Sam Groth for a place in the last 16.
Third seed Murray, the 2013 champion, was equally dominant, taking just one minute longer than Federer to see off Dutchman Robin Haase, the world No 78, 6-1, 6-1, 6-4.
Murray caused some amusement when he threw his wristband into the crowd, where it hit the head of All England Club chairman Phillip Brook - who then handed it as a gift to Prince Charles' wife Camilla, the Duchess of Cornwall, who was sitting next to him.
"Normally you see who catches it. Then the Duchess opened up her bag and my wristband was in there," Murray said. "So he obviously had given it to her."
The Scot next faces experienced Italian Andreas Seppi.
Czech sixth seed Tomas Berdych, the 2010 runner-up, defeated French wildcard Nicolas Mahut 6-1, 6-4, 6-4.
- AAP