Bravo saved all three Portugal spot-kicks to send Chile into the final after the match had ended goalless after 120 minutes.
Arturo Vidal, Charles Aranguiz and Alexis Sanchez were all on target to fire Chile to a 3-0 shoot-out win, but Bravo was singled out for special praise by Pizzi.
"Fortunately, Claudio was amazing in the penalty shootout, the players who scored were amazing and I think we deserve to be in the final," he told a news conference.
"Nobody wants to be in that situation. You never know what is going to happen. But when Claudio was able to stop the first effort and Arturo scored, we calmed down a little.
"Claudio had analysed his opponents very well, he was very well prepared and that's why we were able to win.
"We needed to consider that penalties might be a possibility. I've had to take penalties as a player and it's not the same in training as in a real semi-final or a final. There are different theories.
"I think anything goes but normally we try to do what has brought us success in previous competitions. We were successful with our style in the Copa America [in which Chile have won two finals on penalties] and we did the same.
"I'm very proud of this team and the players are very proud to represent Chile in every single tournament. We are very humbled by the big responsibility we carry.
"I hope we'll be able to keep working the way we are and keep having so much success in Chilean football."
Chile were denied a clear penalty in the second period of extra-time and hit the woodwork twice in quick succession through Vidal and Martin Rodriguez soon after.
"I think we could have scored in the 120 minutes but we had to wait for the shootout, and then we did it well," added Pizzi.
"The shoot-out needs players ready to do a good job. It's a very tense situation.
"Our goalkeeper had the virtue of seeing what the player was going to do. So it's true that there was luck but I wouldn't say it was only luck."