England coach Steve McNamara said he was "frustrated" following his side's 16-14 Four Nations loss to New Zealand.
The side followed up last week's narrow defeat against Australia by losing by two points in Dunedin.
They now need Samoa to defeat the Kangaroos by fewer than eight points on Sunday if they are to reach the final.
"We were a fingernail away last week and a width of a goalpost on a couple of occasions this week," McNamara told BBC Sport.
"We're still in it with a chance if Samoa win but we're desperately close."
|England's Four Nations permutations|
|England through: If Samoa defeat Australia by fewer than eight points|
|England out: If Australia win, if Samoa win by more than eight points|
|If Samoa win by exactly eight points: It would go down to tries scored; England currently have 10, while Samoa have eight.|
England needed to win by 10 points to guarantee themselves a place in the final and went 8-6 ahead before the Kiwis hit back.
Despite failing to gain revenge for last year's agonising World Cup semi-final defeat against New Zealand, McNamara praised the efforts of his youthful squad.
"To apply themselves the way they have done and to attack the competition the way they've done is a credit to them," he said.
"Both teams were absolutely out on their feet. There was nothing left at the end.
"It was an unbelievable Test match. We'll come back strongly from this."
New Zealand skipper Simon Mannering conceded his side were fortunate to come out victorious in a tough encounter.
"They played some great footie, shifted the ball and chanced their arm and defensively put us under a lot of pressure," he said.
"I thought we scrambled pretty well.
"We probably let some tries in that we should have stopped but we're just happy to get the win."