The German club lost the second leg of their last-16 tie 3-2 to Galatasaray at home to go out of the competition 4-3 on aggregate.
"It's an enormous disappointment," he told UEFA.com. "We had enough chances to win the game, and we gave them their goals. We can only blame ourselves for not having given absolutely everything in the first half. It wasn't enough.
"When you look at both legs, then of course the disappointment is all the greater. We were the better team in both games, but Galatasaray scored more goals today and deserved to go through.
"The things which have made us strong in recent weeks were missing a little today. In spite of that, we've played a great Champions League campaign, and can take many positive things from it."
Schalke are currently fourth in the Bundesliga.