Fernando Torres profited from an error by City goalkeeper Joe Hart to seal a last-gasp 2-1 victory and keep Chelsea two points behind Premier League leaders Arsenal.
Mourinho explained that he went to celebrate the winning goal with his son who was sat among the season-ticket holders and apologised if City staff took offence at his gesture.
|13/8||Chelsea are 13/8 with Bet365 to beat Arsenal on Tuesday|
"I think Chelsea is guilty because I want to buy a season ticket for my son and they give season tickets for my son behind the opponent's dugout," Mourinho told reporters.
"They have to change and give my kid tickets behind my dugout. I went for him, I went for him, I promise that I went for him and next match you will see him there again.
"This is the drama of the last minute. I beat Manchester City in the last minute with Real Madrid [3-2 in last season's Champions League], I slid on my knees and I destroyed my trousers.
"If they [City] believe that my son is there, great. If they don't believe, I apologise if they feel I did something wrong."
Mourinho also had no problem with Pellegrini's decision to go down the tunnel following the whistle, claiming he rarely engaged in post-match pleasantries during his time at Real Madrid.
"He lost the game in the last minute and I have sympathy with that," he said.
"In other cultures and other countries we shake hands before the game and that's enough. At the end of the game we don't. In Madrid, normally I never did it so I don’t feel it is a lack of respect.
"If he was sad because of the result I understand, if he was sad thinking I did something wrong, I accept that too, so no problem."
Asked about Mourinho's actions in the post-match press conference, Pellegrini replied: "I don't expect a different way to celebrate from him. It's normal.
"No, I didn't shake [his] hand. I didn't want [to]."