The Bavarians were held at Old Trafford but the winger says the Red Devils were never going to be easy pickings, despite their poor form in the Premier League.
Nemanja Vidic opened the scoring just before the hour mark at Old Trafford but Bastian Schweinsteiger volleyed home soon after to secure the visitors a precious away goal, though the midfielder was subsequently sent off, thus ruling him out of next week's second leg in Bavaria.
Bayern had only failed to win two of its previous 2014 competitive clashes going into the game but Robben is not concerned that the team failed to sweep aside the Red Devils, who are currently seventh in the Premier League.
"In the end, we can be satisfied with the 1-1," the Dutchman told NOS. "At least it's better then 0-0. We scored an away goal, so that's a positive thing. I didn't like it that people from outside underestimated United. The media were talking about them as though they would be easy to beat. I mean, after all you're playing against United at Old Trafford.
"Of course they're struggling in the Premier League, but that doesn't count on an evening like this. I expect a same kind of match next week. We have to move the ball quickly and find the space. We didn't create many major chances, but we're satisfied with 1-1. Next week we have to give it our best again."
Pep Guardiola helped guide Bayern to a second consecutive Bundesliga title already this season and, with the DFB-Pokal and Champions League still in the club's sights, Robben hailed the coach's impact since arriving last summer.
"It's great privilege to have him with us, he has great influence on our work," the winger added to Mediaset Premium. "He's giving us decisive assistance for the conquest of trophies."
United will hope to replicate or better Tuesday's result when it travels to the Allianz Arena for the return leg next Wednesday in a bid to reach the last four of the European competition.