Guardiola claimed City's penalty, awarded after a foul by Virgil van Dijk on Leroy Sané, should not have been their only one of an otherwise uneventful game at Anfield.
A 0-0 draw, but Mahrez was not spared for costing his side three points.
The Algeria global and Gabriel Jesus had stepped up to take the penalty, before Guardiola sent Benjamin Mendy to give Mahrez the duties.
'The usual taker is Sergio Aguero but he wasn't there. "It happens, so we had to move on", the England defender said.
As a striker, Gabriel Jesus - like other players in his position - often jumps at the opportunity to take clear chances, such as penalties. Maybe when we won 2-1 at City, they pushed us in our own 18-yard box and we didn't know exactly how to come out.
That's led to plenty of speculation about problems in the side, with this scoreless display making it four games without a goal for one of their famed attacking trident since all three have been at Anfield. I thought how we defended was brilliant.
Fulham, who equalized through Andre Schurrle, have the worst defensive record in the Premier League and have now conceded 21 goals this season. "The start of the game was fantastic".
Ross Barkley scored his first goal for the club since joining from Everton, with Eden Hazard and Alvaro Morata also netting. "They play for that", Guardiola said. It is so hard to defend so I am really happy how we did it.
Southampton manager Mark Hughes said he believed they paid Chelsea "too much respect" and pointed to a first-half miss by Danny Ings, who blasted over from a couple of meters, as a game-changer. We played very strong and hard today and missed some chances. We were back on track even after we had to change Milly [James Milner] which you never want to do, especially in the first half. We controlled much better than in the past, and with the second balls, on which they are masters.