The Chile international reached the milestone in Saturday’s 2-0 victory over Rayo Vallecano, surpassing former Barca goalkeeper Pedro Maria Artola’ record of 560 minutes, set in 1978.
And Bravo, who arrived from Real Sociedad in the close season, was particularly pleased with the side’s reaction following Tuesday’s 3-2 Champions League defeat to Paris Saint-Germain.
"I’m happy with the record. This is not an easy ground, and they created chances," he told the club website.
"But I was more pleased with the way the team played in general, more than the record.
"Criticism aside, the important thing was to win, and relax. We made corrections after the match in Paris and you could tell. I’m fully satisfied with the game.
"I always have to be ready to intervene when called upon. I wasn’t thinking about the record, I was thinking about the game and working hard not to let in goals."
Defender Jeremy Mathieu added that the record was one earned by the whole Blaugrana defence.
"This was really a record for the whole team because the defence starts with the attack," he said.
"We have all worked hard for this clean sheet."
Saturday's victory was Barca's sixth in seven league outings this campaign, leaving them two points clear of Valencia - who defeated reigning champions Atletico Madrid 3-1 this weekend - at the top of La Liga.