Greece had to settle for a place in the World Cup qualifying play-offs as their bid to overhaul Bosnia-Herzegovina at the top of Group G ended in disappointment, despite a 2-0 victory at home to Liechtenstein on Tuesday.
Greece claimed a comfortable win thanks to a goal early in the first half from Dimitris Salpingidis and late in the second from Giorgos Karagounis.
But they always needed Bosnia to slip up in Lithuania and their rivals' 1-0 win ensured they remained in second place. The two teams finished the pool level on 25 points, but Bosnia's vastly superior goal difference proved key.
Fernando Santos' side now need to come through a two-legged play-off against another second-placed side to ensure their place in Brazil next summer.
Greece went into the match knowing they would by relying on a favour from Lithuania to claim top spot, but were at least able to settle any early nerves of their own with the opening goal after only seven minutes.
Salpingidis slid home a low finish into the right corner from close range to break the deadlock.
Panagiotis Kone fired over the top from way out, while at the other end goalkeeper Orestis Karnezis had to be alert to tip Sandro Wieser's shot around a post.
Martin Stocklasa's shot from the resulting corner was then blocked by Dimitrios Siovas.
That was a rare moment of promise for the hosts, but they themselves were struggling to add to their lead.
Kostas Mitroglou's shot was saved by Peter Jehle, who produced a better save to tip away Georgios Samaras' header from Karagounis' corner.
Salpingidis then mis-hit a shot from inside the area over the bar.
Dimitrios Siovas fired wide from close range before the hosts finally doubled their lead 80 minutes from time.
Karagounis curled a 25-yard free-kick into the top corner to at least make their result safe.
Lazaros Christodoulopoulos almost added a third with another long-range effort, but it was well kept out by Jehle, who also parried a Alexandros Tziolis shot as Greece finished on top.