While City's much-vaunted £51million arrival from Borussia Dortmund managed just 16 touches in 90 minutes and missed an open goal from six yards late on, Alvarez made an instant impact.
By contrast the 22-year-old Argentinian, signed for £14m from River Plate in January but loaned back to the club until this summer, had just two touches in 32 minutes as a second-half substitute but still managed to score to briefly make it 1-1.
"Obviously, I'm very happy for scoring my first goal with City, but that stays aside because it wasn't the result we wanted to start the season winning the trophy," Alvarez, who played both off the right and through the middle with Haaland at the King Power Stadium, told City TV.
"Always I try to give my best in training, I've shown I can play different positions at my clubs and with the national team.
"I can offer alternatives to the team with this versatility, I can offer different solutions and I want to give my best to help the team.
"It's tough, obviously we didn't want to start this way. We don't like to lose. We need to keep working.
"It's going to be a good season to fight for all the trophies and we need to carry on working this way.
"Liverpool have shown in the last years how good they are. They're a great team with great players. So is City.
"It was a good test to start the season, we played well and played at a good level but we need to keep working to get the results."