© PA Photos
Ireland had the early chances, being denied two penalties in the opening five minutes. Despite the missed opportunities, the home side continued to look the more threatening.
Greece had had few chances before Jose Holebas struck from the edge of the box to give the Euro 2004 champions the lead.
Ireland were forced into an early substitution after 34 minutes, as Glenn Whelan picked up a thigh injury.
The two sides exchanged heated words as they left the pitch at half-time.
James McClean took an optimistic strike from 30 yards which went well wide.
In contrast, Greece struggled to get the ball in the final third, with little work for Ireland keeper David Forde.
Despite having more than twice as many shots as the visiting side, Ireland were unable to level the scores.