Rangers created a host of presentable chances against the Seagulls but once again fluffed their lines in front of goal.
And they were made to pay when Brighton struck twice late on through Leonardo Ulloa and Stephen Ward.
"We dominated possession, particularly in their half. But the longer it stays 0-0 the more prone you are to conceding a goal to an odd slip," said goalkeeper Green.
"We dominated the chances and have come away with a 2-0 defeat. It's immensely frustrating and disappointing.
"But that's what happens at this level. If the chances come your way and you don't take them you leave yourself susceptible, one defensive lapse is going to cost you.
"It's a little picture of our season. Sometimes we haven't created chances but this time we did and we weren't clinical enough in that area."
Rangers' automatic promotion hopes are rapidly disappearing - they are now 10 points adrift of Burnley in second.
But Green refuses to give up on making the top two, although he admits it may take something drastic to get there.
He added: "We are still looking to get into the top two. We're looking to win every game that we've got left between now and the end of the season.
"Why should we give up? We could all of a sudden find our shooting boots and score 10 goals a game, and (Burnley strikers) Danny Ings and Sam Vokes get crippled and Burnley's goals dry up!"
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- Leonardo Ulloa