Alvarez scored twice in the second half to inspire a City fightback in the group stages.
Having trailed Red Star Belgrade 1-0 at half time, City turned on the afterburners and won 3-1 by full time.
"Yeah I'm more than happy to help the team," said Alvarez post-game to the club website.
"We created a lot of chances tonight. It wasn't just Erling [Haaland] who couldn't find the net.
"But, I'm very happy to help the team and keep going.
"We're playing very well together. It helps that we're winning and playing very well at the moment.
"I'm doing my best to adapt to this new position and to keep growing and to try and be the free option that is available."