Midfielder Gundogan admits pressure had grown on the team because of those failures in Europe, despite regular domestic success.
“It means a lot,” said the German. “We have obviously struggled in the last few years to achieve what we (have now) achieved. We always failed in the quarter-finals.
“It is releasing and something we deserved, something we deserved already, maybe, in recent years. So it is special now to be in the semi-finals.”
City were given a scare in the second leg at Signal Iduna Park, falling behind to a superb goal from impressive England international Jude Bellingham.
That levelled the tie at 2-2 on aggregate but City fought back to win 2-1 on the night, and 4-2 overall, with a penalty from Riyad Mahrez and a fine strike from Phil Foden.
“We didn’t play well in the first 15 minutes and we were a little bit afraid,” said Gundogan, who reached the final with Dortmund in 2013.
“Dortmund were active and I guess they deserved the first goal. Then we adapted a couple of things in our game and I think we dominated after their goal.”
The result maintained City’s quest for an unprecedented quadruple.
The Premier League leaders and League Cup finalists now turn their attention to their FA Cup semi-final against Chelsea at Wembley on Saturday.
“I don’t like to talk about the quadruple because there is still a long way to go,” said goalscorer Mahrez. “You have to take it game by game.
“Saturday is the FA Cup semi-final and we have to go and win. Then it is the Premier League and then the final of the Carabao (League) Cup. One game at a time and we will see where it takes us.”