Dame N'Doye's 89th-minute header consigned Rangers to defeat at the KC Stadium after Charlie Austin had equalised in the first half following captain Joey Barton's red card for lashing out at Tom Huddlestone.
The London club are only out of the relegation on goal difference as a result of that setback, but goalkeeper Green believes the character Rangers showed at Hull bodes well for their relegation battle.
He told the club's official website: "It's always disappointing to concede goals, especially at the end when you can't respond or do anything about it.
"But we have to pick ourselves up now and get on with it.
"It's going to be tight [down the bottom] until the end of the season. But if we put in more performances like that, we’ll be OK.
"Everyone dug in. It was a magnificent performance to come from behind, when you're down to 10 men that's hard enough. Then it was a cruel blow at the end.
"There were a lot of tired bodies at the end – everyone gave their all for the shirt. It was a fantastic effort. We had a centre-forward [Charlie Austin] playing left midfield. We had people putting in shifts all over the place. I didn't really have to make a save up until the 89th minute.
"Unfortunately, it wasn't to be come the end of the game. It's frustrating for everyone involved but we have to take heart from a performance like that."
