The Chilean coach is looking to steer his third-placed side back to winning ways at home to Sunderland on Wednesday after their title chase stumbled with a home defeat by Chelsea, who now top the table, and a draw at lowly Norwich City last week.
Not surprisingly, Mourinho, who often provokes and antagonises other managers and memorably said last week that "everything I say or do is mind games", has looked to increase the pressure on the big-spending 2012 champions.
After each manager labelled the other team as being title favourites by virtue of how much they had spent in the transfer market, Mourinho hinted City were not operating within the same UEFA Financial Fair Play guidelines.
He then turned his attentions to City's Ivory Coast midfielder Yaya Toure, who aimed an off-the-ball kick at Norwich striker Ricky van Wolfswinkel in Saturday's 0-0 stalemate at Carrow Road but escaped any FA punishment.
Pellegrini, who Mourinho replaced as manager of Real Madrid in 2010, sought on Tuesday to draw a line in the sand under their latest dispute.
"I answered just once to Mourinho because if you remain in silence always, people may agree with those things," he told reporters.
"He started talking about referees and Financial Fair Play, I don't think it is the way to go about things. I will not continue every week talking about things that for me are not important.
"These are not mind games because I don't think managers can be affected by those kind of things, but I will not answer any more on Mourinho."
City, who are two points behind Chelsea and one behind Arsenal, are looking to rediscover their scoring touch after drawing a blank in their last two games, having blasted 68 goals in their opening 23 league fixtures.
Despite having a bulging squad, Pellegrini feels their recent blip has been down to injuries to key players.
"Our recent displays are partly down to injury problems - we also have had (strikers) Alvaro Negredo and Edin Dzeko playing while not fully fit," he said.
"I am not concerned that we haven't scored in the past two games. I have no doubt we will begin scoring goals again soon...
"It's going to be very hard but the team with the strongest mentality is the one that will win the title.
"I maintain the race for the Premier League will go to the last game or two - nobody knows what will happen but that's my opinion."
On the injury front, Pellegrini said playmaker Samir Nasri and midfielder Javi Garcia had returned to training, but defender Matija Nastasic is out with a slight knee problem.
Midfielder Fernandinho and top scorer Sergio Aguero will not return to training for another week.
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