The defending European champions booked their place in a third consecutive semi-final with a 3-1 victory in Munich on Wednesday, progressing 4-2 on aggregate.
After controlling possession throughout the first half the hosts were shocked into life when Patrice Evra's thunderous left-foot drive put United ahead.
Bayern immediately responded with a goal 22 seconds after the restart through Mario Mandzukic, before Thomas Muller and Robben finished the job.
"We played well in the first half," the Netherlands international said. "(But) the first 10 to 15 minutes of the first half was a disaster.
"We were so slow and you can't do that in the Champions League because you will be punished - and we were.
"The goal was a wake-up call, because we went on to score three goals.
"Our goal is to reach the final. We will get one more opponent and our task is to beat them."
Fellow goalscorer Muller felt the Bundesliga champions had done enough to progress to the last four, and praised the way they responded to Evra's strike.
"It was a very intense evening," he said. "Thankfully we managed to score the equaliser right after Manchester took the lead.
"I think we deserved to progress.
"It took some patience but thankfully we managed to do enough in the end."
Bayern are joined in the semi-finals of this season's competition by Atletico Madrid after they eliminated Barcelona, while Chelsea and Real Madrid booked their places on Tuesday.
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