Pellegrini, who quit the Spanish club to take over at the Etihad Stadium this summer, has promised to improve City's brand of football.
The Chilean guided Malaga to the quarter-finals of the Champions League last season and it appears he wants City to follow the same formula for success.
Milner told City TV: "So far we have worked very hard, more on the defensive aspects of the game and changing how he wants us to set up as a team.
"It will take a bit of time to get everyone on the same page as to how he wants us to play and get that, but once it clicks - I think you can see the jobs he has done at his previous clubs.
"We have watched videos of his previous teams doing it to get prepared and see exactly how he wants things doing, as well as doing it on the training field.
"You see the organisation and the record Malaga had in the Champions League last year was really good defensively.
"With our record in the Premier League and the players we have, hopefully we can keep improving."
City began their pre-season preparations in South Africa and have now travelled to Hong Kong to participate in the Barclays Asia Trophy, along with fellow Premier League sides Tottenham and Sunderland.
Pellegrini has left the tour to return to Chile due to the death of his mother but is expected to rejoin the team in due course.
Assistant managers Brian Kidd, who had a spell in caretaker charge at the end of last season, and Ruben Cousillas Fuse have taken over in his absence.
Milner feels disruption to the squad has been kept to a minimum.
Milner said: "Obviously the manager is new anyway, he is still getting to grips.
"Ruben and Kiddo took over. We are used to changes and things like that, so we just get on with the job in hand.
"Hopefully everything is all right with the manager."