Mourinho's latest salvos concerned the decision by the Football Association not to take action against City midfielder Toure over an off-the-ball incident at Norwich last weekend, and calculations over the London club's transfer spending.
These came after Pellegrini responded to Mourinho's claim that Chelsea were the "little horse" of the three teams in the title race by saying they were "little, but rich".
Pellegrini had also suggested Mourinho was continually telling lies about City - there had been previous remarks about Financial Fair Play and luck with refereeing decisions - in the hope that some became established as the truth.
Pellegrini had previously refused to get involved in such tit for tat and the experienced Chilean, who clashed with Mourinho during their time in Spain, wants to revert to that position.
Manuel Pellegrini: "I answered just once to Mourinho because if you remain in silence always, (people) may agree with those things.
"He started talking about referees and Financial Fair Play, I don't think it is the way (to go about things).
"But just once. I will not continue every week talking about things that for me are not important.
"No, I don't think those are mind games. I don't think any managers can be affected by those kind of things.
"I repeat, I don't respond to things Mourinho says every week because he will continue every week to try talking about things that are not from football.
"I suppose the FA acts the way they think is better for all the teams. I trust in the FA and I trust in referees."
1 Chelsea 56 27
2 Arsenal 55 22
3 Manchester City 54 41
4 Liverpool 50 33
5 Tottenham Hotspur 47 0
6 Everton 45 11
7 Manchester United 41 10
8 Newcastle United 37 -2
9 Southampton 36 7
10 Swansea City 27 -3
11 Hull City 27 -5
12 Aston Villa 27 -9
13 Stoke City 26 -14
14 Crystal Palace 26 -16
15 West Ham United 25 -7
16 Norwich City 25 -18
17 Sunderland 24 -13
18 West Bromwich Albion 23 -8
19 Cardiff City 21 -25
20 Fulham 20 -31
Tuesday February 11
19:45 Cardiff City v Aston Villa
19:45 Hull City v Southampton
19:45 West Ham United v Norwich City
20:00 West Brom v Chelsea
Wednesday February 12
19:45 Arsenal v Man Utd
19:45 Everton v Crystal Palace
19:45 Manchester City v Sunderland
19:45 Newcastle United v Tottenham
19:45 Stoke City v Swansea City
20:00 Fulham v Liverpool