Reports in the media suggested that the relationship between manager Pellegrini and Kompany had soured because the Chilean had sided with Fernandinho over his captain following an argument at half-time of the 2-1 loss at Anfield.
Those rumours were quashed by Fernandinho, who stated that he and Kompany were merely discussing the match rather than arguing.
And Pellegrini, who left Kompany out of his starting XI for the team that beat Leicester City in the Premier League champions' last outing, was keen to stress that the issue has been overstated.
"Inside the dressing room we didn't have any problems," he said ahead of Saturday's match at Burnley. "There was no bust-up and it is not important to talk about it.
"We don't have any problems with players in the squad. It was a normal thing, it's not important. There is no problem."
Pellegrini also once again answered questions on his own future after reports emerged that his agent had suggested a move to Napoli could be on the cards.
But the former Malaga boss insists he intends to see out at least the rest of his contract.
"My future is very easy," he added. "I have a contract here until June 2016 and I will finish my contract here. And if I can extend my contract I will. When I sign a contract I always try to finish it.
"If I'm not happy, maybe you try to finish before, but I'm very happy."
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