Luis Enrique's league leaders surged ahead after 55 seconds through in-form striker Luis Suarez on Saturday, but their opponents proceeded to push them back for much of the opening period.
Bravo was on hand to crucially keep out a 10th-minute penalty from Dani Parejo, while Andre Gomes hit the post for Nuno Santo's men.
It was left to Camp Nou hero Lionel Messi to complete the win and score his 400th goal for Barcelona in stoppage time, but Bravo refused to accept his share of the plaudits.
"There are specific moments when goalkeepers must intervene and save the situation," he told GolT after the game.
"When you have a penalty, before it a lot is going through your head, but the first thing that comes to mind is to stop it."
Barcelona touched their brilliant best during Wednesday's 3-1 UEFA Champions League quarter-final first leg win against Paris Saint-Germain and Bravo believed those efforts might have taken their toll on his team-mates.
"[Valencia] were a very good team in every department and made life difficult for us on several occasions," he added. "We came [into this match] on the back of a big effort in Paris.
"Sometimes you all have to pull together when the game isn't going your way, especially when you arrive on the back of a game like Wednesday's.
"Now what we have to do is think of ourselves, go step by step and maintain at [this] level. This victory leaves us all very happy."
