Green dived to his left to keep out Jermain Defoe's spot-kick after the former Hammer had been felled by Lucas Neill.
West Ham had taken the lead in the first half through Carlton Cole after a dreadful blunder by Younes Kaboul allowed the home side to create a simple chance for the striker.
But Michael Dawson spared Kaboul's blushes with a 66th-minute header and England goalkeeper Paul Robinson kept Spurs in the game before Defoe squandered the chance to get one over on his former club.
Curbishley insisted Green had redeemed himself after failing to deal with the free-kick which led to Dawson's leveller.
"It would have been harsh if we had been done in the last minute like that," he said.
"Green redeemed himself for their goal. I am delighted for him because he has been fantastic all season.
"He's come out the game a lot happier. He's been playing well all season and that's all he can do.
"He's been very consistent but I thought Robinson made some good saves today and a draw was a fair result.
"The night before the game we looked at Tottenham's last two penalties which Keane had taken and he had put them in two different places.
"But obviously Defoe took this one and he put it in the same place he did last year, so perhaps that's why Green decided to go that way.
"Green said sorry for the first goal because when you come for the ball you've got to come and get it but what he did at the end of the game made up for it."