Les Parisiens were beaten on penalties on Wednesday night after the match had ended 1-1 between the teams.
"This is a disaster. This is the worst game in my reign, the worst," Ancelotti told Canal+
"I'm sorry, I'm very sorry. It's my responsibility. Our attitude was not good enough. When a team goes on a field with a bad attitude, it's the fault of the coach."
PSG return to Ligue 1 duties on Sunday when they entertain Nice.