City overcame Borussia Dortmund with a 4-2 aggregate win in the quarter-finals.
It is only the second time they've reached this phase of the tournament, and Gundogan says the players feel relieved.
"It means a lot," said the German, who was also at City when they went out at the last-16 stage in 2017.
"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."