The afternoon's action at Goodison Park ended on a sour note with players from both sides becoming involved in a skirmish and Everton substitute Tim Cahill - who appeared to get into a confrontation with Newcastle's Yohan Cabaye - being sent off for his part in it after the final whistle.
Referring to the incident, David Moyes said: "He (Cahill) says he was called something by Cabaye. I don't know what happened after that.
"My only thought was, (Newcastle midfielder) Cheick Tiote had four fouls after he got booked, and when he made the fourth there was a nod to get him off because he'd had too many.
"I thought the referee could have maybe shown a bit of common sense at the end and given him a yellow card."
Cabaye later apologised for his part in the incident which saw Cahill dismissed.
He said: "I would like to apologise for the cross words I exchanged with Tim Cahill which resulted in his red card and my booking on the final whistle.
"It was unnecessary and, regrettably, the result of frustration and disappointment, all in the heat of the moment. It is out of character and for that I am sorry.
"We have had a fantastic season at Newcastle United and already I look forward to next season, the Premier League and the Europa League.
"Finally, a huge thank you to our fans who have been magnificent all season."