Milner scored for the second game running, with Sergio Aguero netting twice and Samir Nasri also on target as City won a league game at Stoke for the first time in 16 years to remain seven points behind leaders Chelsea.
City’s supporters also noisily implored Milner to stay beyond the end of the season, with the England international, 29, still to commit to a new contract.
“When you are trying to sign a contract you need both parties to agree to it, so maybe that’s why it’s not so easy to get it signed,” said Pellegrini after Wednesday’s game at the Britannia Stadium.
“But I repeat, the most important thing is that the club wants Milner to stay here, and he has to decide what he wants to do with his future.”
Milner headed City back in front in the second half after Aguero and Stoke striker Peter Crouch had traded goals before the break.
The goal was Aguero’s first in seven games either side of a month out with a knee injury. He then added another from the penalty spot — his 21st goal of the season — before going off with a back problem.
Pellegrini said afterwards that he expects the Argentina international to be fit for City’s next league game against Newcastle United on February 21.
“When Sergio has more minutes, he will return to his normal performance level,” the City manager said.
“It’s very important for Sergio to be fit. If he can be fit for two to three months in a row, we can see again what a good player he is.
“I hope this year he won’t have any massive problems with the knee issue he had and we hope he will play every game between now and the end of the season.”
– ‘Not thinking about Chelsea’ –
Aguero’s double helped City to record a first victory in six games and although Chelsea’s last-gasp 1-0 success over Everton preserved their seven-point lead, Pellegrini felt his side had registered an important win.
“We needed this victory,” said the Chilean. “Stoke are a very tough team.
“I think in the last three games I have played against them in charge of Manchester City, we scored just once, so to score four goals here is very important and we’ll see if we can continue this way in the future.
“We’re not thinking about Chelsea. Of course, if they had lost points it would have been good for us, but the first thing for our team is to recover the feeling of being a good team, a solid team, and that was the target here, and we did that.”
Stoke’s defeat was only their second in 10 games — a run that has helped them reach their highest points tally in the Premier League at this stage of a season.
Manager Mark Hughes had no complaints about the final outcome, although with the score at 0-0, he justifiably felt his side should have had a penalty when Milner blocked a goal-bound Crouch header with his arm.
“We caused them a lot of problems and clearly should have had a penalty. You need key moments to go for you against the top sides, but unfortunately we didn’t get it,” he said.