Dortmund came from a goal down to secure a 2-1 win and open up a 10-point gap over fifth place with five games remaining.
"We would have put ourselves under immense pressure in view of qualifying for the Champions League next season if we had lost today," Klopp told reporters. "We wanted to avoid that at all costs and this was a big point. We showed an incredibly good mentality.
"It's something of a Champions League legend that it's just hard to play the first half the weekend after a Champions League game. Our main problem in the first half was the number of unforced errors - that was horrific.
"It was just simple things - giving the ball to our opponents, and that's deadly against a side like Wolfsburg, so we were lucky. The second half was a different game and, with our individual quality and the pressure we put them under, that then looked really good."
Dortmund sit in second place in the Bundesliga table.