Carsley assumed the position of England Under-21 coach on an interim basis, taking over from Gareth Southgate who resigned after England's loss to Spain in the Euro 2024 final.
The 50-year-old had emerged as a front-runner for the post after leading England to victories over Ireland and Finland in his first two games in September.
But Carsley came under fire after his tactical experiment backfired in Thursday's embarrassing 2-1 loss to Greece at Wembley.
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Immediately after that Nations League tie, Carsley said he will "hopefully" be returning to the under-21s once England have played their next three matches, starting with Sunday's rematch with Finland.
He then appeared to backtrack, suggesting he wasn't ruling himself in or out of contention.
Asked ahead of the Finland game if he had applied for the job, Carsley told talkSPORT: "No, I didn't formally apply for it."
The FA posted an advert for the England men's senior team head coach job on its website shortly after Southgate departed.
The closing date for applications was August 2, with Carsley named interim boss on August 9.
Pushed on why he had not applied, Carsley said: "I have been doing the under-21s and I am really happy with my job.
"I am an employee of the FA and I was asked to take the senior team, which is a privilege. It was the proudest moment of my career.
"I am really honoured with the chance to manage the senior team. I am in a really fortunate position in that I am on the inside and I can see how much potential this team's got. It is one of the best jobs in world football.
"There aren't many jobs where you've got a chance of winning. I believe the coach that comes in has got a really good chance of winning and we deserve the best one that's out there."
England have arrived in Helsinki needing a win to get back on track in their bid to catch Group B2 leaders Greece.
Former Everton midfielder Carsley is not fretting over his future as he focuses instead on preparing his team.
"I don't see this as an audition at all," Carsley said. "I see it as simple as I was asked to take the team for three camps.
"It wasn't with a view to anything, it was literally do your best, try as hard as you can and look after the players and that is what I am doing."
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