Asensio struck twice as Villa reached the quarterfinals by winning 2-0 on Friday night.
He said afterwards: "We are really happy. It was not an easy game. We knew it was a difficult game.
"I'm very happy for the goals, for the win. we're in the next round, that's the most important
"I'm very happy with the teammates, with the staff, they give me a lot of confidence, so I try to do my best on the pitch and it's going well and I want to score more to give more to this team, to this club and this is my objective.
"Marcus (Rashford) is a top player. We are together not so much but I know what he wants to do, where he passes and I am very happy to have Marcus and all of the teammates.
"We have to keep pushing, we are in the right way. Next step is Champions League and now the focus is there."