The Germans progressed on the away goals rule despite going down 2-0 on home soil this evening, and the Dutch international believes that the Gunners should feel hard done by.
He told Sky Sports News: "All compliments to Arsenal, they did a great job and for them it is disappointing.
"We are happy in the end that we are through. It wasn't our night, but at the end you have to accept that you are through and be happy."
Robben also said that he hopes this evening's defeat will serve as a "wake-up call" for his team ahead of the season's run-in.
"I think the last few weeks, we have played some terrific football but you always have to be focused and concentrated on your own game," he said.
"I hope this is a wake-up call because everyone was speaking about us and saying it couldn't be any better, so maybe this is good for the future."