The Fulham assistant manager was reportedly so furious with Rodgers he left the home bench just 10 minutes into the 3-2 defeat and spent the remainder of the game in the stands.
Rodgers had allegedly told the former Chelsea and England star to 'sit down' following an exchange of words with visiting defender Daniel Agger, but Wilkins insists the duo are now 'sound as a pound' after making up following the final whistle.
"There was no bust-up at all," said Rodgers. "Ray is one of the nicest guys I have met in football. It was just a disagreement on the side over something that took place in the game, but that was all it was.
"They have a good staff at Fulham. Rene (Meulensteen) has taken over a very difficult job and he and his team did very well the other night.
"They are fighting for their lives so it can get a wee bit heated but anyone who knows me knows that is not how I work. I normally concentrate on the football but obviously I protect my team and people."
Wednesday's victory saw Liverpool close to within four points of Chelsea at the top of the Barclays Premier League, prompting Chelsea boss Jose Mourinho to claim the Anfield side are now favourites for the title without the distraction of the Champions League.
However, Rodgers refused to be drawn into any exchange with the Portuguese insisting his objective for the team remains to 'finish as high as we can'.
"In the last 18 months we have built and developed at this club and we'll continue along that route," he said.
"For us the objective was to finish as high as we could and I think what we have shown is in the Barclays Premier League that you need energy and commitment to be near the top of the table, and you need quality.
"We have all three components within our team. At the moment we are full of confidence, our belief is high, our performance level is consistent and, like in the Fulham game where we came back from a goal down twice to win, we showed we have real character."