The Ligue 1 leaders lost the shoot-out 4-1 after Zlatan Ibrahimovic and Thiago Silva missed their first two spot kicks.
The game had finished 1-1, Javier Pastore putting the capital club in front after eight minutes before Saber Khelifa levelled a minute before half-time.
To make matters worse for PSG they finished the match with 10 men, with Thiago Motta sent off in the 118th minute.
Ancelotti was quoted on the Ligue 1 website as saying: "We were a bit full of ourselves and misplaced too many passes, lost the ball too easily.
"Tonight was a disaster and our worst match of the season. The attitude of the team wasn't right.
"You can lose a game but tonight we didn't show any character."
Ancelotti spared none of his team from the criticism, adding: "Some players played for themselves and tried difficult things. I'm angry with the whole team.
"The season's not over and we need to give everything in every match."
Ancelotti, taking the blame for the defeat, also praised the performance of Evian's players.
"Evian's attitude was good and they deserve to be in the semi-finals. If your team doesn't show the right attitude then it's the coach's fault."
Pastore preferred to concentrate on the battle for the Ligue 1 title rather than reflect on the Coupe de France exit.
He told the club website: "This isn't a failure. We lost a match of football, that's all.
"When we don't play well and our opponents defend well, that can happen. We are eliminated from the Coupe de France but there is still the championship up for grabs. Evian were a very good side this evening."
Midfielder Marco Verratti added: "Tonight, we weren't able to make the difference. Now we have to turn our attentions back to Ligue 1 because we want to win the title."
Evian coach Pascal Dupraz is dreaming of making the final and an appearance at the Stade de France.
He said: "We hung in there and we qualified. We're one match away from the Stade de France and I think we're dreaming.
"Ever since the round of 64 game against Amiens in January I'd told the players we were going to go to the Stade de France.
"You need a bit of luck along the way. I think we played well in the first half but suffered afterwards."