The 50-year-old was appointed as Gareth Southgate’s interim successor for England’s six Nations League games across September, October and November.
In his first two games as England boss in September, Carsley guided the team to two 2-0 victories over the Republic of Ireland and Finland.
But he suffered his first setback last Thursday when England were beaten 2-1 by Greece at Wembley.
Reports after the game suggested that Carsley, who guided England’s Under-21s to victory at the European Championship last year, is not interested in taking the job on a permanent basis.
Speaking after England’s win in Helsinki on Sunday, Carsley indicated that he is not the ‘world-class coach’ that the national team needs.
Asked if he wants to take on the job beyond November, Carsley replied: ‘Yeah, I’ve not really thought that much about it.
‘I know I keep saying the same thing – my remit was to do six games, really happy with that, privileged position that I’m in.
‘I’m really enjoying it, didn’t enjoy it for last two days, it was hard work, I’m not used to losing in an England team, I don’t take losing very well.’
Asked directly about the reports claiming he doesn’t want the job permanently, Carsley replied: ‘I think people are always going to try to put their chips on one side. I’m totally in the middle.
‘My bosses have made it totally clear what they need from me.
‘This job deserves a world-class coach who has won trophies and been there and done it. I’m still on the path to doing that.’
When asked about Carsley’s comments, former Arsenal and England striker Ian Wright said: ‘I think he’s being very honest.
‘When you look at him, I believe him. He doesn’t think he’s ready.
‘He knows his remit, he’s got the six games, I admire him, I admire what he’s doing, I admire the choices he’s made because he knows what he’s capable of doing.
‘Like he said, he’s not used to losing which is really cool to listen him to because the Under-21s are so good. But what’s good about it is he’s getting an opportunity an opportunity to have a go at this which he’s very, very privileged to do, very privileged to get that chance.’
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