Pardew was incensed by referee Mike Jones' decision to disallow a stunning strike by Cheick Tiote for offside in their 2-0 defeat to City at St James' Park on Sunday.
Tempers later flared on the touchline and Pardew had angry words with his opposite number, firing an expletive-laden rant at the Chilean.
Pardew has since apologised for his actions and Pellegrini has played down the matter, but the FA has issued a warning to the Newcastle boss.
"We have been in contact with Alan Pardew and reminded him of his responsibilities," said an FA spokesman.
Pellegrini was not unduly concerned by the verbal volley, but more with his opposite number's running battle with the match officials as City claimed a 2-0 win.
Speaking after the match, he said: "I'm not surprised because I think it's impossible to complain about every decision of the referee during the match.
"I know they were playing at home and they have an advantage in that sense, but it's impossible for the referee if you are complaining at every decision.
"That was my only problem with Alan, but nothing important."
Pardew was contrite after discovering that his comments had been clearly audible, and apologised to the City boss.
The 52-year-old said: "I hear that it's been picked up a little bit, and I apologise for my comments 100 per cent.
"It was a heat of the moment thing. We just had words that we always have as managers, to a degree. I have apologised to him and fortunately for myself, he has accepted that."