He also paid tribute to Lionel Messi, who came off the bench to play a big part in Barca's performance after going 1-0 down on the night.
"[The coaching staff] are very happy and proud of our team," he told UEFA.com. "Tonight's game was very difficult; we were playing against a great side.
"We went into the match with a lot of players missing but we showed the necessary class to achieve our objective. We're very pleased and, again, proud to be through to the semi-finals and for having overcome PSG.
"We had an agreement with Messi and in the end this was put into practice. He is such an important player and his mere presence proved the key. He demonstrated that competitive ambition and hunger he has."
Barca are 13 points clear at the top of La Liga.