Klopp said that even though his side did exactly what he wanted from them before the game, the number of chances they missed made it touch and go whether they would get through.
"Basically we did everything right today and in the end we still got so many things wrong," he told UEFA.com. "It was incredible how many chances we created against unbelievably compact opponents who also defended with passion.
"It was even more incredible how we managed to miss those opportunities. We twice had a situation where someone failed to kick the ball when it was already on the goal line and Robert Lewandowski also managed miss an open goal. In the end we required a scrambled shot by Kevin Grosskreutz - but it's a great feeling."
Dortmund topped Group F from Arsenal, who finished second.