England were beaten 19-12 by France and Les Bleus will now meet Wales next Saturday in Auckland after taking advantage of a shambolic showing by England which could yet spell the end of Johnson's reign as manager, with his contract set to expire in December.
First-half tries from Vincent Clerc and Maxime Medard propelled France, apparently in disarray following last week's loss to Tonga, into a 16-0 lead.
Ben Foden responded with a touchdown in a better second half for England but France edged further ahead with a drop goal from Francois Trinh-Duc.
And although Mark Cueto wrestled his way over the line for a second England try in the closing minutes, England limped out of the tournament.
Asked about his future, Johnson said: "I'm not getting into that conversation now. It's not the right place or the right people or the right time.
"We'll see. I'll give it a couple of days, assess myself and how we've been."
Although for the likes of Jonny Wilkinson, Simon Shaw, Mike Tindall and captain Lewis Moody the defeat likely spells the end of their World Cup careers, Johnson believes England's future is bright heading towards hosting the 2015 tournament.
He added: "I believe this team's best days are ahead of it. A lot of them are at their first World Cup and they're better for the experience.
"We left ourselves with a far too much to do. It's brutal.
"France ultimately deserved to win."
England, who won all four group games to top Pool B, had set a semi-final appearance as their minimum requirement and fell short.
For the third time in World Cup history - after 1987 and 1999 - England go home having failed to progress beyond the quarter-finals.
Johnson was bullish, believing his side had begun the match well.
He added: "I thought we actually started the game pretty well when we had the ball. We got a five-metre line-out.
"I think the key thing in the first half was probably two things - their kicking game, their aerial game. They probably reclaimed a lot more of their kicks than we did.
"They won that battle that led to territory and then we had poor defence on the edge twice.
"We said in the week these guys will test you and be more clinical on the edge than anyone we've played - we've played fairly direct teams so far.
"That was the case. Our defence wasn't good enough. A couple of mistakes, two tries and it was very much up hill."
England went close to a try in the dying moments of the first half, but Wilkinson's pass failed to find intended target Chris Ashton.
France, meanwhile, were ruthless.
Johnson said: "With the ball we created two or three real chances in the first half, made some breaks and couldn't finish them off. That was the difference.
"They scored their two tries, we should've had two, we didn't have any.
"The one right before half-time would've made a huge difference.
"We didn't get it so we were chasing the game."
Johnson lamented mistakes in attack which cost his side the opportunity to hit back quickly.
He added: "I think the guys were very confident at half-time that they could fight their way back into the game.
"When eventually we scored (through Foden) we needed to score again pretty quickly and probably took a little bit too long to get a second one.
"We turned the ball over in their 22 a couple of times in the second half when if we had retained it we were really building pressure and momentum.
"That was the story of our night - those mistakes killed our momentum. And they put theirs away early.
"I'm proud of the way the guys fought back in the second half. Their effort was fantastic, but we left ourselves with far too much to do. It's brutal.
"That's what World Cups are. We talked about that. One team goes home with a smile, for everyone else it ends in tears for them.
"I'm just disappointed for all the players, particularly the guys that won't get a chance again.
"These are great opportunities to get somewhere special and we haven't taken it."
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