The Catalan giants defeated Atletico 2-1 at the Camp Nou to move three points clear of their title rivals in the league table.
The visitors hit the lead after just 10 minutes through Koke but finished the match with nine men after defenders Filipe Luis and Diego Godin were both sent off.
By then, Barca had already taken the lead through goals from Lionel Messi and Luis Suarez, but Bravo had to be at his best to deny Saul and Antoine Griezmann to ensure the home side took the points.
Bravo said Atletico's spirited performance was typical of what he had come to expect from Diego Simeone's side, but was happy with how his team handled the pressure.
"It was a difficult game. We knew that they have a very clear game plan," the keeper told Movistar Plus.
"Atletico play a very tough style and that was no surprise to us. We knew how we had to play against them. I’m happy we got the three points.
"We needed to put some daylight between us and a direct rival in the league.
"We anticipated it because they have players who are capable of doing that.
"There are days when you can deal with it and days when you can’t. We didn’t get that feeling today.
"The most important thing is that we were able to get on top of the game. We are going well in all three competitions but we are focused on the day-to-day.
"We have to dig deep to win these games when things aren’t going all our own way."
Bravo admitted it was slightly disappointing not to score a third goal against just nine men, but said the important thing was taking the three points.
"We couldn’t get that third goal that would have allowed us to relax a bit, they moved well and it was hard for us to break through," he added.
"But we managed to stamp our authority on the league."