Cech, who is retiring at the end of the season, kept a clean sheet as Arsenal beat Rennes 3-0 on Thursday to move into the quarter-finals 4-3 on aggregate.
The 36-year-old goalkeeper may have lost his Premier League place to Bernd Leno but Cech has started six Europa League matches in Arsenal's run to the last eight.
Unai Emery's side will find out their next opponents when the draw is made on Friday and Cech is hopeful the Europa League title can prove a fitting final chapter for his career.
"My dream goes on - my dream is to retire with a trophy in my hands," Cech told Arsenal's website.
"Today we gave ourselves the chance for me to finish like this. There's a long way to go but with performances like that, we can compete."
Arsenal became only the second team since the rebranding of the Europa League to progress after losing the first leg of a knockout tie 3-1.
Pierre-Emerick Aubameyang opened the scoring in the fifth minute then crossed for Ainsley Maitland-Niles to level the tie on aggregate, the Gabon international later scoring a second-half clincher.
"We said that if we were meant to go out, we'd go out with a big performance," Cech added. "Sometimes you give a big performance, you do everything right, you are unlucky and you can go out.
"When you perform at the level we did, you know that you have a chance to go through. As soon as the game started, you could see the way the team played and fought together.
"You know that you are giving yourselves a chance. We scored goals at important times and kept a clean sheet, which is what you need in a game like that.
"This game was a tricky situation because at 2-0 up, you're through, but they just need one goal. You know that you need the third goal regardless, and even then, if they score once, you're going to extra time.
"The 3-1 loss away put us in a very difficult situation, but we knew how to deal with that and we got what we deserved."
Aubameyang celebrated what proved the winner by wearing a Black Panther mask, with Cech confirming the move was pre-planned.
"I think he's been talking about pulling it out at the right occasion," Cech said. "He could have got his hat-trick, so he probably won't be happy for himself, but when you score two goals at a crucial time, this is what we need."