Webb - who refereed the 2010 World Cup final - took no action over Balotelli's apparent deliberate headstamping of Parker but subsequently said that if he had seen the incident he would have sent the City player off.
However Mino Raiola, Ballotelli's agent, took issue with Webb's claim.
"I am very angry with the referee, because he lied," Raiola told Italian station Radio Radio.
"The TV images clearly show that the referee is no more than a metre away and that he is looking towards the incident, how can he say that he did not see what he was looking at?"
Regardless of Webb's intervention after the match Balotelli is staring at a four game suspension after being charged with violent conduct by the Football Association (FA) on Monday.
He will begin it on Wednesday - thereby missing the League Cup second leg semi-fnal tie with Liverpool and three Premier League games - should he not appeal the charge.