The Gunners were eliminated from the Europa League by Villarreal on Thursday, losing 2-1 on aggregate over two legs.
They currently sit ninth on the Premier League table with four games remaining, seven points behind sixth-placed Tottenham.
"I think that the problem was that we didn't take our chances," Leno said. "Overall we were the better side. In the first half in Villarreal we were not on our level and that is what beat us.
"In the first half of the first leg we were not at our best but in that second half and today we put everything in. But it was not enough, not good enough.
"A semi-final experience is very important but this is no excuse. We had enough chances to go through. We needed just one goal. It's too easy to say it's just experience.
"It's very hard for all of us. Also for the fans. We are all sad. Hopefully we can make next season better than this season but this season isn't over and in our final four games we must fight for this club and show that we love this club."