Tevez, who left United for City last summer, celebrated his opening goal in front of substitute Neville, who responded with an abusive finger gesture while warming up on the touchline at Eastlands.
Flashpoint: Neville (inset) gestures at Tevez
Tevez, who scored twice on Tuesday night as his new club Manchester City beat United 2-1 in the Carling Cup semi-final first leg, told Sportsmail he wanted to make his point after Neville had claimed in the run-up to the game that United manager Sir Alex Ferguson had been right to let him go.
Tevez said: 'I thought Gary Neville had been disrespectful by talking about me like that. He cannot possibly know the full story of what happened at Old Trafford. I was honourable at all times and I think it was wrong of him to talk about another footballer in that way.
'For me, to celebrate in front of him was not malicious. It was just banter. That is what the game is all about. I didn't see if he did anything back.
'I wear my heart on my sleeve but I also have utmost respect forother players, especially the ones at United. I have won five trophiesat that club and made a big contribution. I had thought and hoped thatthey would show respect back.
'But people get carried away by thecelebrations. These things get the crowd going and help the team. Iexpected Manchester United supporters to give me a hard time. I hopedthey wouldn't but I thought they would.
'I did not celebrate in front of them and I thought that was decent. I really am not being malicious against Gary.
Kids play: Carlos Tevez's celebration was inspired by a big-eared cartoon mouse
'Should I score in the second game next week then I will celebrate with equal enthusiasm and I am sure - if Gary does - he will do the same.'
Neville is currently under investigation by the FA after his gesture towards Tevez was caught on camera. Already on a warning after what were seen to be inflammatory celebrations as United beat City in the Barclays Premier League last September, it seems inevitable the 35-year-old will be hit with a charge this time.
For Tevez, Tuesday was an emotional night and he admitted that his 'cupped ears' celebration that followed his second goal was aimed at Ferguson and the United board who failed to offer him a permanent deal at Old Trafford when he wanted to stay a year ago.
Tevez explained that the celebration is known in Argentinian football as the 'Topo Gigio' - named after a big-eared cartoon mouse popular on TV in Italy and South America - and was brought to the football arena by Tevez's international team-mate Juan Roman Riquelme when they played together at Boca Juniors.
'For me, I admit it was aimed at the Manchester United management. There is a message there but, no, it was not malicious', said Tevez.
'I respect everybody at United. The players and the manager. But these things are part of the theatre of football.'
With former team-mate Wayne Rooney trying to put him off as he prepared to take the penalty that brought City their equaliser, it certainly was a pressure moment. Rooney appeared to be urging Tevez to 'hit the post' but last night the 25-year-old said: 'Yes, he was saying things but I was trying to block it out. It didn't affect me.'
Tevez has scored 17 times for the club he joined for �25m in the summer and believes supporters are now seeing the best of him after he was restricted by a knee problem earlier in the season.
'Mark Hughes asked me to play as other players were injured so I was having injections to get me through. It was causing me great pain and making it hard. It certainly had an impact.
'When I started to read that I wasn't doing well that was difficult for me as people didn't know the full story. Only now are they seeing the real Carlos Tevez.'
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