Mahrez missed the 86th-minute spot-kick, almost sending it into the second tier of the Anfield Road stand, after Virgil van Dijk had tripped Leroy Sané in the penalty area.
Gabriel Jesus, Mahrez’s City team-mate, had appeared keen to take the spot-kick but Pep Guardiola later said he had overruled the young striker.
Mahrez, however, contradicted his manager on this point, telling reporters: “No, I took the decision and took the penalty. That’s football.”
Liverpool vs Manchester City player ratings
Show all 23
The Algerian has now missed five of his last eight Premier League penalties, having not scored from the spot in the league since Leicester City’s 2-2 draw with Middlesbrough in November 2016.
Mahrez insisted that he will not allow this latest miss to bother him, despite it denying City a statement win and a first victory at Anfield since 2003.
“I made the decision to shoot in the middle – the ball went up,” Mahrez said. “Now I have to look forward. It’s part of football – sometimes you score, sometimes you miss.
“The most important part was that our performance was very good today,” he said. “We deserved to win, but sometimes it’s important not to lose, as well.”
Mahrez added: “It won’t affect me at all. Everyone misses penalties, even big, big players. Of course I wanted to score to help the team to win.”
City at least avoided defeat, having lost twice at Anfield last season, and Guardiola admitted to slowing the game down in order to neutralise Liverpool’s dangerous attack.
Mahrez believes City showed a different side to their game at Anfield, tightening up at the back without sacrificing much in attack.
“We were very strong and we showed that we can do both," he said. "We can have the ball but be strong as well. It was a good draw and I think we deserved to win.
“It’s very important. We have to take this with us in the future. We showed that we are not just a team that likes to play and leaves big spaces – we are also a team that wants to be strong defensively, and that’s what we showed today.”
Join our commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies
Join our commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies