The Chelsea manager accused Pellegrini of getting his sums wrong when he suggested Mourinho may have fallen foul of the financial fair play regulations during the transfer window.
Pellegrini was responding to allegations from his Chelsea counterpart that City had benefitted from a number of dubious refereeing decisions throughout the season.
Mourinho has again hit back after a weekend in which his side moved top of the Premier League with a 3-0 win over Newcastle while City were being held to a goalless draw at lowly Norwich.
"What I would like to say that Pellegrini was talking about the money we've spent," said Mourinho.
"I think he's a fantastic coach, and I respect that a lot, and on top of that, outside his football career, he's an engineer by academic formation.
"I don't think an engineer needs a calculator to do [Juan] Mata £37million and [Kevin] De Bruyne £18million, so that's £55million.
"[Nemanja] Matic is £21million and [Mohamed] Salah is £11million. That's £32million, so 55 minus 32 is 23. So Chelsea, in this transfer window, generated £23million.
"It's easy to understand that this is working with financial fair play, fair financial fair play.
"There are no arguments against that. This is what we're doing. Others aren't doing the same. We are building a team for the next decade, if possible. They have a team to win now because they don't have a team for 10 years.
"They have a team for now, for the next three or four. So experience, potential, power, not worried about Financial Fair Play because, in the summer, they just spend... We don't need a calculator for this. It's easy. Plus 23.
"He has a fantastic team, fantastic players, is a good manager. Has lots of experience, so it's not a problem for him. 13 matches are 39 points, and that's an eternity in a league.
"He's been speaking about winning four competitions, so there's no reason to change the speech.
"But the only thing that is funny that he keeps saying he never responds to Mourinho, he never comments about Mourinho. He said that in Spain, too. So, he's changed."
Mourinho admitted the Fair Play rules had stopped him, for now at least, from pursuing Edinson Cavani and Radamel Falcao.
Asked to confirm this was the case, he said: "Correct. Because of transfer fees and salaries. Players are not just about transfer fees, but big wages. Of course there's a certain profile of player we don't go near."
Chelsea travel to struggling West Brom on Tuesday night, and Mourinho is wary that teams lower down the league can still have a big influence on the destiny of the title.
"Maybe the teams not in the top four will be very influential in the league," he said.
"Normally, people are pushed to say Chelsea against Arsenal, or Arsenal against City, or Liverpool against City. These are the matches that decide things. But maybe they aren't.
"In other leagues, it is like that. Madrid v Barcelona decides the title. Benfica v Porto decides the title. It's not the same situation here. The title is decided match after match.
"Every game is important. If we don't win tomorrow, it's not just about the title contenders to jump to the leadership again.
"It's also about Tottenham to win, Everton to win, and closing also the gap. At this moment, every point is important."
Petergriffin- I don't believe that either Manager has cracked, I just believe that Pelligrini is an unwitting participent in a situation that Jose designs specifically to get everyone talking about whatever it is he wants them to. By breaking his policy of 'not answering Jose' to try and set the record straight he is just playing into Jose's hands and further fuelling the fire. It may have no effect on the pitch or perhaps it can carve out a slight advantage if the feathers of one camp are some what ruffled. If the City players react in a similar fashion to their fans who feel the need to take a massive chomp out of Mourinho's bait and flood the comments section of websites like this with all their responses then I would say perhaps it does get under their skin- Mourinho is effectively trolling half the time and I think opposition camps would be better off to completely ignore him but that is just my opinion. As for Chelsea titles chances- I think we all know Jose is painting the picture of us being underdogs to ease the pressure, we are of course will in contention. That said, we finished well off the pace for the last 2 seasons and whilst we are certainly improving I do not believe we are at the level of City who are a much more rounded and complete team at present. I predicted City would win the league at the start of the season and I still believe it's yours to lose.- mhlgate13