The Leeds United midfielder feels the Boys in Green played well and "were comfortable" in their narrow defeat to Austria, which effectively ends their World Cup campaign
Speaking to RTE after the match, Green explained that the players were disappointed at how their opponents struck late to record victory, adding to the misery of Friday's 2-1 defeat to Sweden.
"Mathematically we can still qualify, but it's not looking the best to be honest," Green said.
"The game against Sweden was a massive result, obviously it didn't go our way, and we just wanted to put on a show here.
"We just didn't take our chances. Obviously they have quality in [David] Alaba, and he just finished it off."
Ireland started brightly in the Ernst Happel Stadion, but Austria improved as the game went on before Bayern Munich utility man Alaba scored the winning goal six minutes from time.
Green feels that the Irish players did not deserve the result after putting in a good display, claiming that Giovanni Trapattoni's side were good value for a point.
"We were a threat up front, with Robbie [Keane] up front, he always nicks a goal," he said. "We gave everything tonight, and it's a bit of a sucker punch, obviously with the lad scoring near the end."
"I thought we felt comfortable, I didn't think they caused us much problems," he added."Obviously in the first half, Alaba got a couple of shots off, only because they deflected into his path, it's not like he broke through us or anything. It's a disappointing result and all the lads are gutted, genuinely."
Ireland still have games against Germany and Kazakhstan left in Group C, and Green believes that the players can pick themselves up to end the campaign on a high.
"We've got a few games left to get a bit of pride, and see what we can do," he concluded.
The Republic of Ireland face Germany on October 11, with a game against Kazakhstan in Dublin four days later on October 15.