The German side annihilated the Spanish giants 4-0 at the Allianz Arena to all but secure their place in the final.
"I think we knew were able to give [Barca] a good competition," the Dutchman, who scored Bayern's third, told ITV Sport.
"We can be very proud, this team has dominated Europe over the last five years and if you beat them like this in such a terrific way you can be proud.
"We fought for every metre and we didn't give them any space to play. They only had one or two opportunities."
The return leg will be played at Camp Nou next Wednesday evening, with Borussia Dortmund and Real Madrid facing each other in the other semi-final first leg tomorrow.