Carlton Cole gave the Hammers hope until the visitors ensured the three points with a late free kick.
Zola refused to blame Green for the result.
He told BBC Sport: "Sometimes it happens that you are playing well but you find yourself losing 2-0. It's difficult to accept but it sometimes happens."
"I'm sure that Robert will come back and we are going to be thanking him for saving a penalty or something like that," explained the Italian.
"We have total faith in him and I have total faith in the whole team."
The Irons boss admitted he was hoping for a late equaliser: "I was expecting something to happen in the last few minutes but unfortunately it happened in the wrong way.
"It's been a game in which I learnt a lot and I hope my players did so too," said Zola. "Sometimes to improve you have to go through bad games like this."