Mane was dismissed 37 minutes into the game at the Etihad Stadium for a dangerous collision which saw goalkeeper Ederson stretchered off.
The Reds star chased down the ball at full speed and leapt with his foot high to control it, only to catch the face of the Brazilian goalkeeper.
City were 1-0 up at the time the 25-year-old was dismissed, but two goals apiece from Gabriel Jesus and Leroy Sane saw them to a comprehensive victory.
And Klopp believes that referee Jon Moss made the wrong call in showing the red card to the winner of August's Premier League Player of the Month.
"I don't think it's a red card, he didn't see him,” the Reds boss told Sky Sports.
“I saw the goalie already and obviously it's not that bad. In the first moment everyone thought it was really bad.
"It was unlucky, it was an accident. The goalkeeper comes out, Sadio wants the ball. To get a red card in a game like this is really unlucky."
He added: "I'm sure people will find enough reason to say it is a red card. I could not even see Sadio Mane touched him."