Green allowed a 25-yard shot from USA midfielder Clint Dempsey to slip from his grasp and over the line for the equaliser in a 1-1 draw.
Green's error cancelled out the opening goal from England skipper Steve Gerrard and leaves the group in the balance for Fabio Capello's side.
Lampard said: "We are all behind Robert, he is a fantastic keeper. Everyone makes mistakes and we are together as a team.
"It wasn't the worst performance in the world but there is always room for improvement."