The Three Lions were sent home after a 2-1 defeat to Didier Deschamps’ men, despite a spirited performance in Doha.
The reigning champions took the lead 17 minutes into the first half when Real Madrid midfielder Tchouameni found the bottom corner from 25 yards out.
The strike into the bottom corner caught Pickford by surprise and it came after a good start from England.
Gareth Southgate’s side battled back and got back on level terms when Harry Kane levelled from the penalty spot just after the interval.
Olivier Giroud struck the winner 15 minutes from time and Kane ballooned another penalty attempt over the bar.
But Keane felt the writing was on the wall after Tchouameni’s opener and he wasn’t happy with the Everton goalkeeper’s role in the goal.
‘It’s a brilliant strike,’ Keane told ITV.
‘[But could the ] keeper could he do better? Yeah, I think so.’
Southgate is set to stay on as England boss, despite the Three Lions’ premature exit.
Gary Neville believes Southgate is the right man to lead England into the European Championships in 2024.
‘I would love Gareth to stay on for another two years,’ said Neville.
‘I’d love him to stay on beyond that whether it be actually as the coach or whether it be in a role in the FA in the future.
‘England in the last 10 years have won youth tournaments. We’ve won a women’s tournament in the summer. We’ve got to the men’s final in the Euros. We’re playing really well.
‘We’ve got a good team of technical players. England is in a pretty good place, let’s be clear about that.
‘We’ve been out of tournaments in disgrace in the last 25 years, thinking what the hell is that what is the future. We’ve got a great future and he is a big part of that.’
MORE : Gary Neville sends message to Gareth Southgate over his England future
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