United had only 26% possession in the first leg at Old Trafford but still managed to come away with a 1-1 draw to take to next week's decisive second leg in Munich.
Dutch winger Robben believes Bayern's away goal could prove crucial but warned that United should not be under-estimated.
Robben said: "It was not easy, as Man United played very defensively and didn't leave any gaps. We wanted to play football but they tried to stop us, just playing on the counter-attack, it was almost like handball.
"Away goals are very important and that's why we are satisfied having come back from 1-0 down, so we'll take the result back home and hopefully finish it off next week.
"I didn't really like the atmosphere before the game because everyone was saying you are going to win it, it's going to be easy.
"No - you play at Old Trafford against Manchester United who are a top team and top players and the Champions League is something different, it's not like the [domestic] league.
"We have to bring in another top performance to beat them and it's going to be very difficult."
Meanwhile, midfielder Toni Kroos played down links with a move to United even though the Germany international has failed to agree a new contract.
He said in Munich's TZ newspaper: "It (Old Trafford) is a beautiful stadium. But I belong to Bayern Munich and that's good.
Bayern chairman Karl-Heinz Rummenigge added: "He will certainly play at Bayern next year. What's beyond that, I don't know."
Bayern's sporting director Matthias Sammer also claimed United should have had Antonio Valencia sent off - he was on a booking when he went into a full-bloodied challenge with Jerome Boateng in the second half, but escaped punishment from Spanish referee Carlos Velasco Carballo.
Bayern goalscorer Bastian Schweinsteiger did see red, though, picking up a second booking for a late foul on Wayne Rooney to rule him out of the second leg in Germany.
Sammer said on Sky in Germany: "If you apply the same standards then I don't know how Valencia stays on. If the referee has a policy, then he must go through with it.
"There's no question that what Schweini did was a foul, but with Valencia there will also several fouls and his outstretched leg against Jerome Boateng. At this level you have to apply the same standards.