Wilkins abruptly left his role as assistant manager on November 11 after being told his contract, which was due to expire at the end of the season, would not be renewed.
The 54-year-old former club captain called in the lawyers and a settlement was reached with the Barclays Premier League champions at the start of this month.
Bad night: Wilkins (centre) during the defeat against Inter Milan last season
But speaking for the first time about his departure, which has coincided with a downturn in form for Chelsea, Wilkins admitted a heated discussion with Abramovich following the club's Champions League exit to Inter Milan last season was not behind his removal.
'I don't think I fell out with him at all,' Wilkins said. 'I think if that was the case, then I would have been removed from my position immediately.
'There wasn't so much a row, there was a discussion. I think everybody was immediately after the game a bit pent up and we'd been knocked out of the Champions League by Inter Milan, who are a very good side and who over two games deservedly beat us.
'I think we're big enough to come away from that situation but we've moved on from there and we've won the double but obviously the owner felt that there was need of a change, and he made that change.'
Hard to take: Skipper John Terry (centre) after losing to the Italians in March
Wilkins revealed that the reasons for his departure as assistant to manager Carlo Ancelotti had not been made clear.
'The reason hasn't been given, so I'm still waiting for that,' he explained. 'But that really isn't a problem as far as I am concerned.
'We always want to know why, but if it isn't forthcoming we've got to get on with our lives.
'I've no problems. I was privileged to be part of something that was very special and was a great adventure.'
Wilkins also confirmed that he was dismissed at half-time during a reserve game, and added: 'These things happen. You just have to accept it, because nothing should ever surprise you anymore in football.'
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