The Germans reached the semifinals after a 3-2 win at the Nou Camp, so progressing 4-3 on aggregate.
Xavi said, "We were trying for some heroics at the end but it wasn't sufficient. We didn't play the best way – in fact, we weren't good tonight. They played well on the counterattack and although their second was a fantastic goal, it stemmed from a very silly mistake of ours.
"Time after time we allowed them to get after us and damage us. It's a huge disappointment – we had our hopes in terms of winning this competition. It's time for us to congratulate Frankfurt. They've deserved this. We had control of the ball but we didn't generate the quality of chances we needed.
"We are out because we didn't play to our level either in the first leg or here. But we played on the right lines. Europe's tough, you pay dearly for mistakes. The key was to make better chances and do them damage with the possession we had."
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