The Dutchman was pleased with how the Parisiens presented themselves while Javier Pastore stressed Carlo Ancelotti's side did a good job, in his opinion
PSG held Barca to a 1-1 draw at Camp Nou on Wednesday after previously recording a 2-2 draw in the first-leg, but the underdogs were eliminated on the away-goals rule.
"Of course we are proud; we did a great job against one of the best teams in the world. We've drawn twice against Barcelona so that's certainly something to be proud of," Van der Wiel told Uefa.com.
"You have to watch out for Barcelona, you can't let them play their game. We had to press them as much as possible and, most importantly, to have the courage to play our own game.
"It could be that Barcelona are a different team when [Lionel] Messi doesn't play. We all know he's a fantastic footballer, he can decide games on his own. But tonight we had the chance to win here. You saw the crowd when he came on and how they reacted. I guess it was a big boost to the team too.
"Of course we leave a little disappointed but most of all we can be proud of how far we have come."
Javier Pastore, meanwhile, was very pleased with PSG's performance as well but admitted that it is nearly impossible to stop Barcelona from scoring.
"We produced a great display," the Argentine added. "We showed that you can play well here and you can attack Barcelona. Unfortunately they found the goal they needed to put them in the last four. [Lionel] Messi was their decisive player.
"Once they scored they were a different proposition. They were relaxed and playing as they like to. It was imperative we stopped them scoring but it seems they always get a goal at Camp Nou."