Despite Manchester City's record-breaking campaign last season which saw them capture the league title with a century of points, Liverpool got the better of City in three out of the four games they played across all competitions.
However, Riyad Mahrez was off target from the spot-kick.
Stones said City were delighted to keep a clean sheet after conceding seven goals in their past two visits - one game in the Premier League and one in the Champions League - but Mahrez's miss took the gloss off their performance.
Sarri, who replaced former Chelsea boss, Antonio Conte in the summer, also reiterated his belief that his team will struggle to close the gap on City and Liverpool this season.
"It is an unbelievable challenge to face Man City and as the last game it makes the challenge even bigger", Klopp said.
'I watched it because I wanted to get the rebound but I was very happy that it didn't go in.
"Last season we lost here, and this season we drew, maybe next season we will win".
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"He did not start in the first 11 today but when he was on he scored within a minute and that gives confidence for both him and us".
Luck was once again not on their side as Guardiola's men controlled large spells of the game but simply couldn't fashion chances when they needed to.
As well as the penalty, Mahrez had the two best opportunities, dragging one effort just wide of the far post and then drawing a smart save from Alisson at his near post.
"We played Chelsea last week, who were excellent". We have played City often and they are outstanding.
Jesus, who replaced Agüero in the 65th minute at Anfield, believed he was supposed to be City's second choice penalty taker behind the Argentina global. "It was really intense and both showed respect for the other team", he said.
"You can not ignore City in the preparation for a City game", Klopp said.
"In training he shoots ideal penalties but sometimes it happens", Guardiola said post-match. They remain on five points, one place above the relegation zone. That was really important to see it agains, to adjust a few things. We defend so well as a team; it starts from the front with the work-rate they put in. I made the decision to shoot in the middle - the ball went up.
"We had our chances as well; it's not as if it was their game for the taking".