Despite qualifying for the play-offs, Northern Ireland couldn't overturn a 1-0 deficit from the first leg against Switzerland.
Over in Basel, Switzerland fullback Ricardo Rodriguez, who scored a controversial penalty which gave them a 1-0 win over Northern Ireland in Belfast last Thursday, made a goalline clearance from a Jonny Evans header late in the game which prevented the tie going into extra time.
For the first 30 minutes Greece were in control, but despite two good shots from Borussia Dortmund defender Sokratis Papastathopoulos and AEK Athens forward Anastasios Bakasetas, the home team failed to get the much-needed early goal.
Greece continued to enjoy more of the ball in the second period but when it came to finishing off an attack, either a pass would go astray or a defender would step in.A shot on the turn by Mitroglou from just outside the penalty area just missed the post with an outstretched Subasic unable to reach it.
"This is a devastating moment but also a very proud moment", said Northern Ireland manager Michael O'Neill, who described the manner of their defeat as "cruel".
Seferovic should have settled it in the 85th minute but instead shot high and wide - and was substituted nearly immediately.
I do, however, share in the frustration of seeing a poor refereeing decision at Windsor Park rob Northern Ireland of a place in the World Cup finals.
A number of club sides, including Rangers, are also said to be monitoring the man who led Northern Ireland to a maiden European Championships in 2016, and it is understood the right club project would be the preferred choice should he leave his current job.
Despite his heroics in charge of his national side, O'Neill's lack of experience at club level is scaring Rangers fans off.
After three years in charge of Irish side Rovers, O'Neill was appointed as Northern Ireland manager.