The City ace and United's club captain exchanged gestures after Tevez had drawn the Blues level in Tuesday night's Carling Cup semi-final first leg.
As revealed by MEN Sport on Thursday, the FA wrote to both clubs to ask them to calm their players down ahead of a potentially volatile second leg at Old Trafford next Wednesday.
But in an interview for Argentina's ESPN channel, recorded before the FA warning, Tevez lays into his former team-mate.
The bad blood began when Neville said in a newspaper interview ahead of the first leg that his manager, Sir Alex Ferguson, had been right not to sign Tevez in the summer, indicating that he was not worth the £25m price City paid.
Tevez responded by signalling to Neville that he talks too much and Neville responded with a crude one-fingered gesture.
Now Tevez has given both barrels to the Red veteran, saying: My celebration was directed at Gary Neville.
He acted like a complete boot-licker when he said I wasn't worth £25m just to suck up to the manager. I don't know what the hell that idiot is talking about me for. I never said anything about him.
Lack of respect I will never show a lack of respect towards anyone. Just as I was running off to celebrate the penalty I had scored, I came across Gary and I said to myself: Shut your trap, keep quiet'.
I didn't go overboard in my celebration and it was directed at Gary, not at Ferguson and not at the fans.
I think he did the wrong thing because I was his team-mate and I never said anything bad about him.
He was saying that Ferguson was right when he said that I wasn't worth £25m, when he was saying this and that. I always respected Neville.
Tevez speaks little English, but he said he had seen Neville's comments in the newspapers on the day of the game.
I was at lunch with the players in the team hotel and all the papers were laid out. I read them well, 'read them', obviously I don't read English.
My team-mates were telling me about it and asking what I thought. And I wondered to myself: What's the moron talking about me for when I never said anything about him, when there was never any issue with us.
It was a lack of respect for a fellow player, apart from the fact that we had won a lot of things together.
You have to do your talking on the pitch. I don't talk much in England mainly because of the language. I don't like to get involved in conflict.
Revenge with City
"I'm happy because I know what I am. Thank God I had the chance to get revenge with City, although there is still the second leg to come. The latest outburst won't please Greater Manchester Police who, after 18 arrests following the first leg and having confiscated several dangerous objects from United fans at Eastlands, are anxious at the rising temperature surrounding the clash and are considering upping their presence at Old Trafford on Wednesday.
Tevez also had a warning for United, who wouldn't comment on the remarks last night, that City are on the march: There are differences between the two teams. Manchester United is a huge team in the city, everyone knows that. But City are making giant strides.
There were also some sobering words for City fans, as Tevez admitted he is not enjoying life in England.
Things are going well for me; the goals are coming, he said. I'm in good shape, I have avoided injuries and that really helps.
As a kid I would never have imagined that I would live in England for four years. I am very happy and contented that my daughter is growing up in a country as developed as this one.
But the truth is that it's very, very hard for me to live here, so far away from my loved ones.
This is my fourth year but I'm not exactly an example of how to learn English; I just can't get it into my head. I'm learning hardly anything, truth be told. I don't go out much, I spent most of my time at home.
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