Sebastian Kehl cancelled out Hulk's opener in the return leg of their last-16 meeting with Zenit on Wednesday, as Dortmund were beaten 2-1 on the night.
Despite the defeat, Klopp's side still progressed to the last eight on aggregate and the coach was delighted to have made it to the next round.
"Sometimes success can hide even behind a 1-2 defeat," he said after the match.
"Borussia Dortmund have to learn that. We are at the quarter-finals again. Up there with the creme de la creme. That's awesome."
Captain Sebastian Kehl echoed his coach's sentiments, insisting his side deserved to progress.
"Perhaps it wasn't our best match, but we have reached the quarter-finals of the Champions League and can all leave the stadium with a huge smile on our face," he told Uefa.com.
"We are very happy going through, as we've had a lot of injuries this season. We never complained about it, but it does cost a lot of energy.
"Despite all this, we deserve to be among the best eight teams in Europe."