The Bundesliga champions held out for a goalless draw in Wednesday night's quarter-final second leg to progress through 2-1 on aggregate.
Victory for Bayern came 24 hours after Barca suffered a 3-0 loss at Roma to crash out of the competition on away goals, and Robben says a wake-up call was provided by the Giallorossi.
"Of course that was a warning," he told reporters. "It shows that everything can happen in football. If you play at this level, you need a top performance. That will be the case in the semi-final.
"We are now in the semi-finals in the Champions League and in the DFB-Pokal. We have to go a bit further. In the semi-finals there are no favourites. We have to see who we get tied up with and then prepare well. There are only good teams left.
"From the outside, maybe 2-1 away felt as if it was almost done but we knew that they have a good team. In the first half we had some trouble in midfield. Then they have quality and they can play. They had a few chances. In the end we had more chances, but what was missing was a goal. We should have scored a goal."
Bayern will learn of their final-four opponents on Friday afternoon, with Liverpool, Roma and Real Madrid joining them as the last teams standing.