The 25-year-old felt he should have been awarded a penalty shortly before the hour mark in Tuesday's game and was shown a red card after making contact with official Serdar Gozubuyuk.
Roda - who already trailed through a Bart Biemans own goal in the first half - were further frustrated by Aron Johannsson's goal shortly after Nemeth's dismissal.
Nemeth has since taken to the club's official website to apologise for his actions.
"After I was knocked over in the penalty area, and therefore did not get the penalty that should have been given in my opinion, I've let myself go emotionally and I barged against the referee Gozubuyuk with my chest," he said.
"It was a mistake and I apologise. This is not like me as a player and I also realise I have let down not only myself but also the team.
"I will accept the punishment that the KNVB has imposed on me."
The news is a further blow to relegation-threatened Roda who are on an eight-match winless run in the Eredivisie.
Nemeth misses crucial games with Utrecht, PEC Zwolle, Feyenoord, NAC Breda and ADO Den Haag.
Technical manager Leon Vlemmings added: "Internally we had a chat with Krisztian about the incident. During that he expressed regret.
"We obviously do not condone this behaviour as a club and accept the penalty imposed by the KNVB. For us the matter is now closed."
