Managerless Leeds have let in five goals in the final six minutes in their last seven games, including Charlton's late winner at The Valley last weekend, and a fourth straight defeat has seen them slip to within five points of the relegation zone.
"It was very disappointing," Green told the club's official website. "It's happened before and we have to cut it out.
"Every time we get into the 90 minutes something has happened and we have to stop it. You can't put your finger on why.
"It is gutting because you're putting so much work into getting a result then that happens, but we have to keep going and carry on."
Leeds take on relegation rivals Sheffield Wednesday in a derby clash at Elland Road on Saturday and Green will not shirk from the challenge.
"We've got a good group here who are more than capable, and we're looking forward to Saturday against Sheffield Wednesday," he added.
"It'll be a tasty game. It'll be tough, all derbies are, and we'll work hard this week to try and get a result.
"You want to finish as positively as possible. We'll step up and hopefully get the three points and carry that on against Burnley."