Mourinho's latest target was Arsenal F.C. manager Arsene Wenger, whom he labelled on Friday a "specialist in failure", and the Portuguese irritated Pellegrini last week when he suggested City were not operating within UEFA's Financial Fair Play rules.
"Jose Mourinho can say what he likes," Pellegrini said in an interview with Spanish sports daily Marca published on Saturday.
"His statements are an attempt to ease the pressure and transfer it to another team," added the Chilean, who also clashed with Jose Mourinho when they were coaching in La Liga.
"I don't think there's much point in attaching too much importance to it," Pellegrini said.
"A lot of the time it is hard not to give in and respond, but to enter into the cycle of personal responses doesn't seem right or good.
"If other coaches want to avoid pressure in case they don't win anything and generate an atmosphere of little responsibility that's their business."
Manchester City F.C. are three points behind Premier League leaders Chelsea with a game in hand and they host the London club in the fifth round of the FA Cup later on Saturday.
Chelsea F.C. won 1-0 at City in the league at the start of the month, when Pellegrini was missing a number of key players through injury.
In his first season in charge since leaving Malaga, Pellegrini said his free-scoring team had not yet reached the level he was aiming for.
"I know that it is my first year but that doesn't take away the pressure," he said.
"On the contrary, I like it," he added.
"It's true that we have to improve in many areas. The first year is when you dissect the team, it's weaknesses and strengths, and you get an idea of what you need."
City host Barcelona in the first leg of their Champions League last 16 tie on Tuesday.