The Toon Army finally managed to break their capital curse with a eventful 3-1 win against The Gunners, but Poll's decisions to send two players off and award the visitors a penalty left Arsenal, notably Thierry Henry, fuming after the final whistle.
Henry is facing disciplinary action after his attack on Poll, but McDermott says that the players should just accept the decisions and get on with playing.
"Newcastle got a little lucky, but you can't tell me Arsenal don't get good decisions playing at Highbury," said McDermott.
"Arsenal had one man sent off in dubious circumstances, but so did Newcastle so that didn't benefit any side.
"At the end of a season, luck always evens itself out and the Arsenal players should concentrate on their next game the minute the final whistle blows because there is nothing you can do about the result then.
"Players should accept results and not act like poor losers. Losing is part of the game and all players must deal with it.
"When it comes to luck, Newcastle have had some terrible misfortune over the years so maybe they deserve a little slice."
Bobby Robson's side now top The Premiership, but McDermott does not believe that the have the squad to go all the way, although he hopes he is proved wrong.
"Like most people, I think Newcastle are probably a bit short. They haven't got the strength in depth Leeds, Manchester United, Liverpool and Arsenal have, but I hope I am proved wrong.
"I would love Newcastle to win the title but, realistically I think the players would feel a place in Europe is more achievable."
Newcastle, meanwhile, will be appealing to the FA to reduce the straight red card that was shown to Craig Bellamy during the game at Arsenal for elbowing Ashley Cole in the face.
The Magpies want the red to be reduced to a yellow card, which would still have resulted in Bellamy being sent off but would result in just a one-match ban instead of the three he is facing for violent conduct.
