The Netherlands international scored in each leg of the semi-final against Tito Vilanova's side, and was delighted that his team progressed to the final at the Blaugrana's expense
The former Real Madrid star opened the scoring with a fine finish past Victor Valdes shortly after half-time, before an own goal from Gerard Pique and a towering header from Thomas Muller late on made it 3-0.
"It surprised me that we could dominate the match today, but we deserve credits for this. We expected a tough game, but it wasn't that tough at all," the Dutchman told NOS.
"It's not up to me to say that we were superior to Barca, but we won both games with our own style.
Speaking to Uefa.com after the game, Robben said: "I think it is a terrific performance, it is a little bit of history.
"To perform like this, against a team who have dominated Europe for the past five years, who have so much quality, it is amazing.
"The most important thing is we play as a team, not only going forward but defensively.
"If you want to achieve something and have results and win competitions at a high level you have to defend as a team."
Robben then gave his thoughts on the prospect of an all-German Champions League final against Borussia Dortmund at Wembley.
"[The final] is going to be a big one. Dortmund have proved over last two to three years they are a very good team."
Fellow Bayern winger Franck Ribery was equally impressed with the team's showing against the Catalans and highlighted their team ethic as the side's key quality.
"Above all, we all work together. We want to do something together and we showed that tonight," the France international told Canal+.
"We knew that if we defended well, we could score goals.
"Dortmund is a team that is not easy to play against and has a little of our style – it will be a good match.
The France international also expressed his desire to finally get his hands on a Champions League winners medal, having twice been a runner-up.
"I've already lost two finals, I do not want to lose a third. We'll play as we played tonight."
FCB captain Philipp Lahm explained that he always thought his team was capable of producing a performance like they did against the Liga leaders.
"It’s not taken for granted to beat Barcelona on their home ground 3-0," he said.
"But I’ve always said that we have special characters in our squad and that we are capable of great things."
The Bavarian giants will face Dortmund in the first all-German Champions League final. The match will be held at Wembley on May 25.