The two sides served up a Champions League classic at the Etihad Stadium on Tuesday, with the hosts eventually running out 4-3 winners.
Benzema scored twice on the night to take his Champions League goal tally for the season to 14.
City were ahead inside the first two minutes, with Kevin De Bruyne scoring the fastest goal ever in Champions League semi-finals history. Gabriel Jesus added a second after 11 minutes but Benzema halved the deficit before halftime.
Phil Foden headed City further ahead early in the second half but Vinicius Junior reduced the deficit straight away with a piece of brilliant individual magic before Bernardo Silva restored the hosts' two-goal advantage.
Benzema added his second from the spot with a panenka penalty to give Madrid hope heading into the second leg at the Santiago Bernabeu next week.
"There are 90 minutes at the Bernabeu for the fans to make a difference again," Benzema told Movistar+. "We leave here with our heads held high to play a good game in the return leg. The fans leave proud.
"We have to keep our heads calm and see what we have to do to improve, a little of everything and especially at the beginning of games."
"A defeat is never good, but we are excited about this Champions League and the important thing is we never give up," Benzema added. "Now we have to go to the Bernabeu and we need the fans like never before to do something magical, which is to win.
"We entered the game without confidence, and that's what happens with an opponent like Manchester City. In this game a little bit of everything was missing."
