Roberto Mancini was unhappy with the performance of referee Mark Clattenburg after Manchester City suffered their first defeat of the season at Chelsea on Monday.
The official then sent off Gael Clichy in the second period before handing Chelsea the chance to win it from the spot after a Joleon Lescott handball.
Mancini had no issues with the Lescott, but he did have problems with Clattenburg for not being so decisive with Silva's claims.
"When we had ten players it was difficult," Mancini told Sky Sports. "We tried to stay in touch but it was really difficult.
"We deserved to score two or three goals in the first half, and if we had scored a second the game would have been different because the sending off was really difficult.
"The turning point was the penalty in the first half. The referee was there. He was really sure in the second half when they shot from five metres at Lescott, but in the first half he was three metres behind Silva and didn't give a penalty.
"This changed the game."
Chelsea boss Andre Villas-Boas had a different opinion, stating that Silva should have been booked for diving. The Blues boss even needed reminding of the incident, initially replying: "I'm surprised you're mentioning it because I don't know what you're speaking about!"
When prompted, he then recalled: "To me it didn't look like he touched him, and if he didn't touch him it should be a yellow card. That's my opinion without seeing it again.
"If it is a penalty, well the other day we had a penalty claim and Phil Dowd didn't give it. So I'm sure Roberto isn't satisfied but every game has a different decision."