Wednesday night's 1-1 draw in Paris guided PSG to a 3-2 aggregate success, with an opening goal from Valencia's Jonas wiped out by an equaliser from Ezequiel Lavezzi.
Ancelotti said: "Over the two matches, I think we deserved to qualify. It was more difficult tonight (Wednesday) than in the away leg. In the first half, we played with a bit of worry about us. Paradoxically, we started to play better after the goal by Jonas and we played well in the second half. The players showed a very good reaction."
And so PSG go forward to a Champions League quarter-final for the first time since 1995, when they beat Barcelona over two legs to advance to the semi-finals.
Milan toppled the Parisians in the last four, but on the evidence of Wednesday night's largely drab performance Ancelotti's team will struggle to make further progress this year.
Club president Nasser Al-Khelaifi wants PSG to become a permanent fixture in the latter stages of the Champions League, and has designs on winning the trophy by 2016.
Al-Khelaifi is more than pleased with the progress that has already been achieved, and was full of praise for the accomplishment of finishing off a Spanish side with bags of Champions League experience.
"We are very happy to qualify for the quarter-finals," he said.
"It was a difficult match for us, but we are now one of the best eight clubs in Europe and it's magnificent.
"Before the match, I was very confident. It was a delicate operation to score tonight but everyone worked hard: the coach and the players."
- Sports & Recreation
- Champions League