The Chilean, making his third appearance of the season, made three one-on-one stops in normal time before making two diving penalty saves in the shoot-out.
Guardiola said: "It was so, so tight - we had chances in the first half, then in the second half we conceded some counter-attacks - they are so fast in counter-attacks.
"Today Claudio gave us the chance to go through, I’m so happy for him, the way he trains, he made a good performance in the game and in the penalties.
"Now we understand how difficult things are. The competition is so complicated, it can take you out of your normal rhythm."
Guardiola added: "Last season was not easy for Claudio, but he is a goalkeeper of a high level, it’s not possible to play with Barca, Chile (without this)… he deserved that performance."
In a match that many thought would be about striker Sergio Aguero and his quest for the all-time goalscoring record, Bravo provided an unexpected twist.
But Guardiola is confident normal service will resume soon for his Argentinian forward.
"Sooner or later he is going to score," the boss said.
"Relax, he is going to break the record… the situation is going to happen."
Guardiola confirmed that Ilkay Gundogan ended the game with an injury concern, with further tests to take place on Wednesday.