The 74-year-old has been in the job since replacing Steve Staunton in 2008 and took the country to the UEFA European Championships last year after narrowly missing out on qualification for the 2010 FIFA World Cup.
But Ireland's hopes of reaching next year's World Cup in Brazil took a major blow when they were beaten 2-1 at home by Sweden in a crucial qualifying fixture last Friday.
The country now face a trips to Austria and Germany before their qualification programme ends with a home fixture against Kazakhstan in October, and Trapattoni believes he will leave his post after those games.
"I don't expect, after this campaign, to go again in the future," the Italian said.
"Over five years, I think we have achieved a good result. We have changed the team, we have improved the ranking, we have moved on players and discovered many others.
"I can continue and help the next (manager) because in this short time, maybe this player or another can show the next manager where he can place his trust and how to develop him."
