The French side were on the verge of pulling off a stunning upset at Camp Nou, but Pedro's equaliser saw them exit on the away goals rule
The Ligue 1 leaders looked set to record a sensational upset when Javier Pastore put them 1-0 on the night, and 3-2 ahead on aggregate, just five minutes into the second half of the second leg at Camp Nou.
However, Pedro equalised soon after for the hosts, who ultimately held on to progress to the final four on the away goals rule.
"Its hard to be eliminated after what we did tonight," Ancelotti told Canal+. "We were a little timid in the first leg and the result [2-2] was not good.
"But after tonight's game, while we feel regret, we also feel pride. We are proud because we did everything possible to win.
"We played well - didn't just defend - and that is why I want to thank all the players. We were so close to winning this game. This could have been a fantastic night for us."
PSG will now have to pick themselves back in time for this weekend's Ligue 1 meeting with Troyes, with les Parisiens looking to extend the seven-point lead they currently hold over second-placed Marseille.