City began their Barclays Premier League campaign and life under Pellegrini with an emphatic 4-0 win over Newcastle last month.
But since then they have been below par, suffering a shock loss at Cardiff and then labouring to a 2-0 win over another of the promoted sides, Hull.
Pellegrini is attempting to implement the club's preferred new system and there have been some uneasy moments, particularly defensively, but Kolarov is in no doubt they will come good.
The Serbia international told the club's website: "We are still getting used to the new coach.
"There is a change in our style but I think we can do much better than last season.
"We'll be looking to do well in the Premier League and Champions League this time.
"We are working a lot on the defence and I feel like we are improving every day.
"I think as we get used to the manager's thinking we will be playing at a high level."
Kolarov was an unused substitute in the first two matches but replaced Gael Clichy at left-back against Hull.
The 27-year-old was linked with a move in the summer but he is keen to stay at the Etihad Stadium.
Kolarov, who scored a superb goal against Wales in midweek, said: "There were a lot of stories in the papers over the summer but I never said that I wanted to go.
"I have two more years on my contract at City so my only focus now is to work hard in training and when I get the chance to play, to do my best and show the manager what I can do."
Some of City's defensive problems have been exacerbated by injury.
Captain Vincent Kompany and new signing Martin Demichelis are now sidelined while Matija Nastasic and Micah Richards missed the start of the campaign.
Nastasic returned against Hull a fortnight ago while it was hoped Richards could be in contention for this weekend's trip to Stoke.
City were also assessing playmaker David Silva after the Spaniard returned early from international duty this week with a thigh injury.