Fabio Capello's side were held to a 1-1 draw by Bob Bradley's team after an early goal from Steven Gerrard was cancelled out by Clint Dempsey thanks to a glaring error by goalkeeper Green.
But Lampard has faith in the West Ham stopper to recover from his blunder five minutes before the interval.
The Chelsea midfielder said: "It was unfortunate. These balls are moving about. I don't know how much the ball moved.
"We were disappointed for Greeny because we are a team and we win, lose and draw as a team.
"It is unfortunate for keepers, They are the last line and, when they make a bit of a boob, it gets picked out.
"But no-one will be pointing the finger. He made a good save in the second half as well (from Jozy Altidore).
"I think he has got the character to bounce back. You are playing in the World Cup so you have to have character because it doesn't always go your way.
"Greeny will have that. I hope so. He is a very good professional. He will work hard and keep going."
Lampard admits England have to improve on their performance against the Americans and win their next two games to ensure qualification for the last 16.
Now they need to overcome Algeria and Slovenia to give themselves a realistic chance of topping Group C.
The 31-year-old said: "Maybe the point will be important but we have to go and win the next two games now.
"All the teams I have seen so far in the World Cup will look to improve and we are the same as everybody else in that way.
"It was frustrating not to get the win. It wasn't a bad performance but we will want to - and we will need to improve.
"We possibly should have won the game. It was disappointing. We created enough chances. We were pretty comfortable until they equalised.
"In the second half we had a couple of chances so it was a bit frustrating not to get a win which would have put us in the driving seat in the group.
"Steven scored early and after that we felt in control of the game. They never really threatened too much in our box.
"It was a bit of a freak goal for them and that gave them a lift going into half-time."