Pep Guardiola’s men held a slender 2-1 advantage going into the second leg in Germany, and fell behind inside 15 minutes to an inch-perfect effort from Jude Bellingham.
And Gundogan was impressed by the manner in which City dug deep to turn the tie on its head and secure a last four clash with Paris Saint-Germain.
He said: “We know how tough this competition is every single year.”
"Everyone has quality, and this Borussia Dortmund team has a lot of quality, on a good day they can beat anyone.
“It’s about staying in the game, your attitude and your personality in that stage of the competition.
“We proved ourselves today that we are ready to fight in the semi-finals.”
While we ultimately got the job done on the night, the nerves were jangling up until Mahrez confidently dispatched the equaliser from the spot in the 55th minute.
Despite our best efforts to get back into the game after Bellingham's opener, the hosts defended doggedly to preserve their crucial lead until Emre Can's handball handed City the advantage.
Gundogan admitted that we were far from our best in the early exchanges, but was pleased with how we responded to the early setback.
“Today was once again about showing character,” he reflected.
“I don’t think we played well at all in the first 15 minutes, we struggled, we weren’t quick enough, we were a bit scared to lose something, I think that was quite obvious.
“But after conceding we started to get better, we were able to hold more possession, keep the ball and create a couple of good chances.
“Then our target at half time was to come back into the game as score the first goal in the second half to get the game back into our hands.
“That’s exactly what we did and we’re proud of that.”
Our 4-2 aggregate victory secures a place in the last four of Europe’s elite competition for the first time in five years, but City cannot rest on their laurels during such a busy part of the season.
Pep Guardiola’s men lock horns with Chelsea in the FA Cup semi-final this Saturday, before facing Aston Villa in the Premier League and tussling with Tottenham for the Carabao Cup title in the following eight days.
But Gundogan insists he and the players wouldn’t have it any other way, revealing that the team are relishing the challenge as the fixtures come thick and fast.
“For me it’s not that difficult because there’s nothing else to do,” he asserted.
“We are professional footballers and we play the game to be successful.
"We want to be successful in every single game, that doesn’t guarantee it but we just try the next one and that’s exactly what we’re going to do on Saturday and then we’ll see.”