But Trezeguet connected on a wonderful cross from Ahmed El Hommady three minutes into stoppage time to book Villa's ticket to Wembley.
Villa goalkeeper Ørjan Nyland was in impeccable form to help deny the Foxes and send the Midlands club to their first League Cup final since 2010.
Speaking after the game, Nyland said: "Crazy. Through the roof. Unbelievable.
"The first 15 minutes, they put a lot of pressure on us. The whole team did well. Then we scored with a great attack. We knew the class Leicester have. .
"They scored late so it looked like it was going to penalties but we got the winner in the end."
Asked was it his best game for Villa, Nyland said: "Yeah definitely. My best one was the first leg. To do it again was amazing.
"I always thought of it [whether he would play] since I played the first game but there's been changes. It was good to get the game and play the way I did. I hope so [he'll start the final]."