After Marc Guehi had found an equaliser for Palace deep into injury-time, the Carabao Cup quarterfinal tie went to penalties.
Neither side missed from the first 15 attempts from 12 yards, until Kepa denied Maxence Lacroix to secure Arsenal the win.
“We are in the next round, we're happy,” he said afterwards. “I think we made a huge effort. We should have scored, I think, a couple in the first half. We played so well. Then the second half was more like 50-50.
“Even like this, we had good chances. We’ve conceded in a couple of games in the last minute so it's something that we have to look at. And then credit to the guys, they took amazing penalties. They keep us in the game, and they give me an opportunity to make a save.”
Kepa also said: “Emotionally, you have to be focused, be strong, because obviously when you concede in the last minute and then you have to go to penalties, you need to 100 per cent be focused on your penalty takers, you need to save. So it was a change of mindset, and it worked.
“We’re prepared for everything, every possible scenario. We were playing against a very strong team, so that can happen.
“So we talked about it before. We have a very good group of goalkeepers, we talk between each other and try to be focused on the next penalty, always the next one.”
A semifinal against Kepa’s former club Chelsea now awaits.
“Right now, if you want a trophy, that's something that we want. We have to fight against good teams. I think both semi-finals, are big games, it's going to be tough, but we'll prepare well the game. We'll be ready and we'll go for it.”