Bayern, runners-up in two of the last three finals, took a first-minute lead through David Alaba's deflected long-range strike before Thomas Muller tapped in a second goal just after the hour mark at the Allianz Arena.
Robben, who started on the bench but was thrown into the action after just 16 minutes due to an injury to Toni Kroos, told Sky Sports: "When we spoke about the game before we said we couldn't concede a goal today, that was the important thing and in the end 2-0 at home, good advantage."
The Holland international drew a fine save from Juve goalkeeper Gianluigi Buffon soon after coming on before then side-footing another good opening wide during a dominant first-half display by Bayern.
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 all over the pitch.
"I think there was a period in the first half, just after I came on, where they made some mistakes and we had some good chances. It was just a bit unfortunate that we didn't score another goal. But in the end, in the second half we scored another one, and good result."
- Sports & Recreation
- David Alaba
- Thomas Muller
- Toni Kroos