The Germans tied the aggregate score at 2-2 after 15 minutes thanks to Jude Bellingham.
But City eventually wrestled back control to win the match 2-1 (4-2 on aggregate) to book a Champions League semi-final against PSG.
"It means a lot to be honest, this club and this team deserve it," said Gundogan post-game. "We are grateful for being in a great competition and reaching the semi-finals for the first time with this team. Obviously we are very happy about it.
"Today once again we showed character, we didn't play well at all in the first 15 minutes, we struggled and we weren't brave enough and were scared to lose something. That was obvious.
"After conceding the first goal we were able to get hold of possession and create chances. Our target was to score the first goal of the second half and get the game back into our hands. That's exactly what we did."