Carsley was appointed as Gareth Southgate's successor on a temporary basis in August, initially for the Nations League campaign over three international windows.
However, the 50-year-old, who stepped up from his role as under-21s manager, has since given mixed messages about whether he wants the job on a permanent basis.
After Thursday's shock 2-1 defeat to Greece at Wembley he said he would "hopefully" be going back to his role with the under-21s before saying the job should be given to a "world-class manager" in a TV interview following Sunday's 3-1 win in Finland.
But just minutes after that, in his post-match press conference in Helsinki, he said he was "definitely" not ruling himself out of the running for the permanent position.
Arsenal midfielder Rice brushed aside suggestions that the uncertainty was unsettling for the players.
Asked whether the squad needed clarity, Rice, who scored the final goal in England's win in Helsinki, told the BBC: "No, not at all. He has been clear with us when he came in... that he was looking after us for three camps.
"With the way he has been and the way we have played, I think he has been unbelievable.
"It's my first time working with him because I haven't worked with the under-21s, but the 21s boys that have come in couldn't speak highly enough of him.
"We as senior players are not surprised but we have said how good he was in meetings and games and how he takes training."
Thursday's defeat to Greece at Wembley, where Carsley played an experimental team packed with attacking players, appeared to be a major blow to his hopes of landing the England job permanently.
But Rice said the players should take responsibility for that defeat.
"We were the problem on Thursday night," he said. "There were too many sub-par performances. It was a different game if we score goals. That is down to us not Lee."
England head to Athens next month trailing the hosts by three points and knowing defeat would end their chances of promotion back to League A as Group B2 winners, though they could still achieve promotion via a play-off.
