City had already had two shouts for penalties - one when Sergio Aguero appeared to be bundled over by Dejan Lovren and one when the Croatia caught Gabriel Jesus with a flailing arm - when Virgil van Dijk tripped Leroy Sane.
City had the flawless opportunity to end their awful run at Anfield but Mahrez, not particularly reliable from the spot, blazed his effort high into the stand.
Klopp, though, was happy with Liverpool's performance against City.
A win on Sunday would be massive for Liverpool both in terms of going back to the top of the Premier League as well as building confidence to carry through the global break and into the next run of fixtures.
The 27-year-old has admitted that City's clash with Liverpool on Sunday will be the Citizens most hard challenge on the road this season.
The Premier League's top two sides face-off on Merseyside in what is sure to be a mouth-watering clash between title contenders.
In a game that saw little goalmouth action, City edged the midfield battle and could have been rewarded all three points via a late 86th minute penalty.
"If you play so quick they are much better than us".
Then after an hour, Van Dijk handled the ball in the box.
That resulted in these free-flowing juggernauts only producing two shots on target each in a goalless draw as they highlighted why both have only conceded thrice coming into this test. You can not defend over 95 minutes, 100 percent but I thought how we defended was brilliant. "He was on the pitch when the first penalty was not given", the City manager said.
The Merseyside outfit came from behind to rescue a 1-1 draw with Chelsea FC at Stamford Bridge last weekend after former Manchester City striker Sturridge netted a late equaliser. We tried to be ourselves all the time and we compete really, really good. What few chances there were fell largely City's way. In that situation they are much better than us.
"It is for both teams really intense what we are doing and both showed respect for the other team". We were close, more than ever to winning here but it is better than last season and we compete really really good.