City's 2-0 win at Newcastle has been overshadowed by a row over a controversially disallowed Magpies goal.
Cheick Tiote thought he had equalised at 1-1 with a superb long-range strike but Yoan Gouffran, stood in an offside position, was deemed to be interfering with play.
Newcastle manager Alan Pardew was incredulous and shouted abuse at Pellegrini, for which he later apologised, in the touchline argument that ensued.
Pellegrini said: "Yes, of course, he apologised at the match, I accepted it.
"When the match finishes, all the things stay there. It doesn't matter in the future so for me, there is no problem about that.
"In football you have experienced a lot of different things. Everyone acts the way he thinks is the best way to do it."