Ochoa, 28, was the star for Miguel Herrera's men as they held the FIFA World Cup hosts at bay in the Group A clash in Fortaleza on Tuesday.
The free agent made a tournament-high seven saves to earn his side what could be an important point.
Ochoa paid tribute to his team-mates, but was also pleased with his individual performance.
"It was a very difficult game, especially playing Brazil on their home turf. When we heard the fans cheering we knew we had to double our efforts," he told Univision.
"Fortunately the team put in a great defensive performance and the whole group earned this valuable point.
"I think it was certainly the performance of a lifetime, as to keep a clean sheet with good saves against Brazil in a World Cup is as good as it gets."
Ochoa kept out a Neymar header in the first half with a diving save to his right and his reflexes denied Thiago Silva's close-range header in the second.
It was the save from Brazil star Neymar that he described as his most difficult.
"That was the toughest, as it was right by the post," Ochoa said.
With four points and an inferior goal difference, Mexico are second behind Brazil in the group, but ahead of Cameroon and Croatia – who meet on Wednesday.
