Matt Targett opened the scoring for Villa, only for the hosts to be pegged back by Kelechi Iheanacho midway through the second half.
But with the game seemingly destined for penalties, Trezeguet got on the end of a delightful Ahmed Elmohamady cross to fire in the winner and send Villa Park into delirium.
Rodgers told Sky Sports: “I thought we were excellent in the game. Their goalkeeper made some outstanding saves.
“We had a nice control in the game. I thought we should have had a definite handball for a penalty.
“By the end of the game I thought only one team looked like they were going to win it.
“I am gutted for the players. We were the better side over the two games.
“The players are hurting and will tomorrow as well.
“It’s tough to take looking back over the two games but congratulations to Aston Villa and we have to move on.”