The 30-year-old wore the captain's armband for the clash and led by example, opening the scoring with a neat header in the seventh minute.
Ferran Torres swiftly made it two, before Gabriel Jesus added a third just before the interval. Rodrigo stroked in a wonderful fourth, quickly followed by a fifth from Torres.
"It's a privilege to be a part of this team, of this group of players," said Gundogan.
"Obviously, when you're able to put performances like that on the pitch then even more. It's a day full of happiness.
"I had a feeling that I couldn't put a lot of power to the ball for the goal because I wasn't sure if the defender in front of me was able to get it or not.
"I just tried to head it towards goal. It was quite close to the goal so the goalkeeper didn't have much time to react.
"I've scored, I just try to be in the positions. I try to smell where the ball will drop.
"I was lucky to get the first goal. It was a good start to the game today. I just try to help the team. I try to adapt as good as possible."
The midfielder also provided his thoughts on City's UEFA Champions League hopes and the upcoming international break.
Watch the entire interview via the video at the top of the page.