The Dutch ace began the UEFA Champions League quarter-final first leg on the bench but came on in the 16th minute after Toni Kroos was injured.
He helped the German side - who had taken a first minute lead via David Alaba's deflected long range effort - then dominate proceedings.
But despite a whole host of chances, they could not get a second goal until the 63rd minute when Thomas Muller tapped in to give Bayern the advantage ahead of the second leg in Italy next Wednesday.
Robben told Sky Sports: "When we spoke about the game before we said we cannot concede a goal today, that is the most important thing.
"In the end, 2-0 at home, is a good advantage."
He added: "I think it was a very good game to watch because both teams were pressing forward and it was almost one-against-one on the whole pitch.
"I think especially there was a period in the first half straight after I came on when they made some mistakes and we were on the counter-attack and we had some good chances, myself as well.
"It was just a bit unfortunate that we didn't score another goal.
"In the end, in the second half, we scored another one, so it is a good result."