Costa has been banned for three matches - ruling him out of Saturday's top-of-the-table Barclays Premier League clash with City - after being found guilty of violent conduct over a clash with Liverpool's Emre Can.
Pellegrini was asked his opinion on the matter at a press conference to preview the game at Stamford Bridge.
The Chilean said: "He is a great player, a very important player.
"He has his character, it is not an easy character, but I hope for him that (with) this punishment - and I am not trying to take advantage for the game tomorrow - it will be a good thing for him to change in the future because he doesn't need to do it in that way because he is a very good player, a top player."
Pellegrini's remarks were unlikely to receive an immediate response from Jose Mourinho as his Chelsea counterpart did not hold his regular press conference on the eve of the match.
Other than that, however, Pellegrini was unwilling to comment on many matters specific to Chelsea for fear of stoking his perceived rivalry with Mourinho.
"I don't talk about Mourinho," he said.
Chelsea go into the match with a five-point lead over defending champions City but, with four months of the campaign remaining, Pellegrini claims it is not a must-win clash.
He said: "I think it is a very important game. It is not the game that will decide the title because after that we have to play for 45 points more.
"If you remember some years ago this club won the title after being eight points behind Manchester United, so in football you never know.
"But it is a very important game and it is important for us to try and close that gap as soon as we can."
City are also without a key player in Yaya Toure due to the midfielder's involvement in the African Nations Cup.
City have not won any of the four Premier League games they have played this season without the 31-year-old and they were also knocked out of the FA Cup in his absence last week.
But Pellegrini feels the game is about more than Toure and Costa.
He said: "I say always the same thing, in this case for Diego Costa or Yaya, big teams with important squads cannot depend on just one player. I think it is a very important miss for both teams but they have other players to replace him."
The Costa issue has taken the attention off Frank Lampard's return to Stamford Bridge.
Chelsea injury list and suspensions
Chelsea injury list and suspensions
1/3 Loic Remy
Mourinho suggested Remy had a chance of playing last weekend against Manchester United, however he was not even on the bench, leading to uncertainty over his availability.
The summer signing from Atletico Madrid has not played since the start of the month when he featured for 12 minutes against Stoke. Whilst there were fears he may not feature again this season, the Spaniard is understood to have returned to training and could even make a surprise outing at the Emirates.
3/3 Didier Drogba
Played last weekend in the win over Manchester United, however he pulled out of a charity match this week with an ankle injury, putting his participation against Arsenal in doubt.
Lampard is Chelsea's record goalscorer and a club hero but was not expected to join their main title rival when he was released at the end of last season.
That has left some uncertainty over what reception the 36-year-old might get at his old ground, but Pellegrini has no doubt what it should be.
He said: "I am sure that Frank Lampard will receive the best reception from their fans that they can do. He is a top player, maybe the most important in their history.
"He gave so many things to that club. If he couldn't continue playing there, he can play here. That is not his fault. I am sure the fans will repeat the reception they gave here to Frank in the first game."
Lampard scored when he came off the bench to face Chelsea at the Etihad Stadium in September but refused to celebrate.
Asked if he should celebrate this time, if he scores, Pellegrini said: "First I prefer him to score the goal. After that we will see if he celebrates or if he doesn't celebrate. If he scores, I celebrate."
Pellegrini intends to approach the game in his usual confident manner, with his sights set solely on victory, and is not thinking about the consequences of defeat.
He said: "We always try to keep our style but I cannot answer you what is in the mind of Chelsea, their manager or their players.
"They play at home, I am sure they want to win, but maybe they can think a draw is a good point for them because they would keep the five points (advantage). But I cannot know what they are thinking.
"I don't feel pressure, never. The only pressure that I feel is my own pressure to try and do my best job."Reuse content