Robert Green allowed a low 25-yard shot from United States midfielder Clint Dempsey to slip out of his hands and over the goal-line for the equaliser in Saturday's 1-1 draw in Rustenburg.
With Slovenia overcoming Algeria yesterday to go top of the group, Lampard is aware England cannot afford any more slip-ups in Cape Town after skipper Steven Gerrard's early goal was cancelled out.
England's vice-captain said: "It's crucial to win the next game. To win against the USA would have put us in the driving seat but we have to believe in ourselves.
"It was the first game - and first games are notoriously cagey. They all have been like that so far in the tournament and we were just unlucky with the goal.
"It felt very comfortable at 1-0. We had got the goal, were knocking the ball about well, were in control.
"It was unfortunate and it was frustrating. Their goal came at a good time for them.
"If they hadn't have scored when they did, then I'm sure we would have gone on to win the game.
"But that's the way it was and we know there is room for improvement still."
Lampard insists Green has the support of the players and he showed his character with a crucial second half save to deny Jozy Altidore a shock winner.
The Chelsea midfielder said: "I didn't need to say much, just 'keep your chin up.'
"We need to stay together as a group and we all make mistakes and unfortunately as a keeper you are the last line.
"The ball moved about a bit. Greeny would be a bit disappointed but he did make a very good save second half.
"You have to support your team-mates, we are a group and we need to stay together.
"We've all been in positions in a game where you don't want to let your chin drop and I think Greeny did that."
Capello has now to decide whether to show faith in Green, who has started nine of the last 12 internationals, or recall either David James or Joe Hart.