The Bundesliga giants suffered a rare off night at the Allianz Arena on Wednesday, and were almost made to pay for that by a resurgent Gunners side.
Trailing 3-1 from the first leg of their last-16 encounter, Arsenal fell agonisingly short in their efforts to overhaul that deficit - with a 2-0 victory in Germany seeing them slip out on the away goals rule.
Robben admits Bayern are relieved to have kept their European dreams alive and believes a humbling on home soil could end up working in their favour.
The Dutch winger told Sky Sports: "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.
"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.
"These are special Champions League nights. In football, anything can happen. It's exactly what we spoke about before the game - we warned each other and said don't let them come into the game because they will give everything. The one thing you don't want is for them to score an early goal, and that's exactly what happened.
"Overall, especially in the first half, we didn't play at our level, we weren't aggressive enough and lost all the second balls.
"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."