The Germans reached the semifinals after a 3-2 win at the Nou Camp, so progressing 4-3 on aggregate.
Araujo said: "What a pity to lose this match – notwithstanding the result, we did what we'd been working on in training. It's a pity because they hit us at all the crucial moments – there are errors you can't commit in European football and that's why we're out.
"We really needed to be more patient in the build up and to concentrate far more when we were facing their quick transition play. We wanted to go through so much here.
"It was a big surprise that so many Frankfurt fans were in the Camp Nou. People will call this a disastrous result for us because we did want to win the Europa League. But we need to get our heads back up immediately – there's still the Liga to fight for."
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