Pardew was seen swearing at the Chilean during City's 2-0 success, which was littered with yellow cards after Newcastle's manager, players and fans were left incensed by a decision to disallow Chiek Tiote's first-half strike for offside. .
"I hear my comments were picked up and I apologise for them 100 percent," Pardew told reporters.
"In the heat of the moment we had words as we managers always have. I have apologised to him. And fortunately he's accepted."
Pellegrini, who thought referee Mike Jones was right to disallow the goal, said troubled brewed on the sidelines after Pardew's continued criticism of the official.
"I think it is impossible to complain every decision of the referee during the match," said the Chilean, whose side went top of the table with the away victory.
"I know they are playing at home and have an advantage in that sense but it is impossible. That's why a problem with Alan but nothing important."
Pellegrini was critical of the referee for not sending off Newcastle's Mapou Yanga-Mbiwa, who was only shown a yellow card after hacking down Samir Nasri in the second half.
Nasri left the field on a stretcher with Pellegrini fearing the midfielder had suffered a serious injury.