"I didn't play," Nadal said. "That can happen when you play an opponent like this. But I don't want to talk about the opponent."
Brown, the world No. 85, broke Nadal's serve at the fifth attempt to win the first set, and he pulled off two audacious lobs in succession to break the Spaniard again early in the second.
Nothing Nadal tried seemed to work in his first match since winning his ninth French Open title. He had a first-round bye at Halle, where he was the top seed.
"The only way I could have tried to do more was resisting with my serve, something I hadn't practiced a lot these days," said Nadal, who was unnerved by Brown's unpredictability.
"For the first four games he didn't put any returns on the court and then suddenly he was playing winners from the return, so it's difficult to analyze these kinds of matches. The only thing I can do is keep working the way that I did the last three days, because I came here, I tried hard, I tried my best."
"I never played against a world No. 1 before, never played him before, so this is just crazy for me," the player with the distinctive dreadlocks said.
Brown said it was too soon to consider he will face compatriot Philipp Kohlschreiber in the quarterfinals.
"I haven't thought about that at all yet. I'm going to enjoy this," Brown said.
Federer began his preparations for Wimbledon by coming from behind to beat Joao Sousa of Portugal 6-7 (8), 6-4, 6-2.
Sousa saved all five break points he faced before taking the first set in a tiebreaker, but the second-seeded Federer raised his level in the next two sets to win the second-round match and move into the quarterfinals.
"It was important to stay calm, and actually it gives me more confidence winning this way than maybe just 6-4, 6-4 and you don't quite know what is going on," said Federer, who acknowledged he was worried after losing the first set.
It was the seven-time Wimbledon winner's first match since losing in the fourth round at the French Open to Ernests Gulbis. He also had a first-round bye in Halle, where he is a six-time champion.
He will next play Taiwan's Lu Yen-hsun, who defeated Croatia's Ivo Karlovic 7-6 (2), 7-6 (3).