"We knew after last season what we needed to do and we have improved, " Robben said.
Robben, by contrast, is already looking forward to the final against their arch German rivals.
"I think it is a terrific performance, it is a little bit of history, " Robben said.
Croatia striker Mario Mandzukic grabbed the opener, turning home Dutch international Arjen Robben's cross.
The former president first contracted tuberculosis in the 1980s while detained on windswept Robben Island.
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But when United's offer for Robben, 20, arrived it was for half that figure.
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Bayern played the better football throughout with Franck Ribery and Arjen Robben hitting the woodwork.
To Nelson Mandela and his fellow prisoners on Robben Island it was a beacon of hope.
This time Chelsea left it even later as Robben's goal kept them just two points behind United.
Kalou then got on the end of a rapier-like Chelsea counter-attack inspired by Didier Drogba and Robben.
But he is unhappy at having had no prior knowledge of Robben's recent visit to Old Trafford.
Robben, just outside the penalty area, chose to stay on his feet and Casillas again denied him.
Messi escaped the attentions of Arjen Robben, but was halted by a clumsy challenge by Chelsea's Spanish defender.
Robben forced a one-handed save from Cesar before Milito gave Inter a two-goal cushion with more superb finishing.
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Giovanni van Bronckhorst, Wesley Sneijder and Arjen Robben each scored to earn a clash with Spain or Germany.
Meanwhile the player's father and agent, Hans Robben, blamed both clubs for the failure to reach a deal.
BBC: SPORT | Football | My Club | Man Utd | Man Utd upset PSV
Dutch winger Robben scored the visitors' second away goal firing home from six yards in the 70th minute.
The experienced and consistent former Lyon star may provide a more reliable influence than the injury-plagued Arjen Robben.
His history of lung problems dates back to when he was a political prisoner on Robben Island during apartheid.
Bayern Munich's goal-scoring duo of Arjen Robben and Franck Ribery (known as Robbery) can make defenders dizzy as well.
Eighteen years were spent on the windswept Robben Island where he contracted tuberculosis.
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He first contracted tuberculosis in the 1980s while detained in Robben Island prison.
Robben did force a decent save from Casillas with a low left-foot strike after cutting inside during stoppage time.
Bayern had taken the lead before half-time, Arjen Robben slotting in from the spot after Franck Ribery was fouled.
Add that to the absence of Arjen Robben and all of a sudden people are asking questions of them.
BBC: SPORT | Football | Europe | Chelsea face their biggest test
"I think we knew we were able to give them good competition, " Robben told ITV following his side's impressive showing.
Robben delayed his shot but, equally, Casillas stood his ground as long as possible and brilliantly saved with his legs.
Robben missed two good chances to put the champions back in front but a tactical switch from Mourinho proved inspired.
Fellow Dutch internationals Ruud van Nistelrooy, Arjen Robben and Wesley Sneijder have all been linked with moves away from the Bernabeu.
Real had been poor and Arjen Robben had their best chance when his shot was steered over by keeper Jose Reina.
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