The Three Lions picked up a 3-1 win over Finland, days after a bruising 2-1 home loss to Greece.
Interim boss Lee Carsley has been vague about whether he wants the permanent job or not.
Rice told BBC: “No, not at all. He has been clear with us when he came in back in September 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.
“He is one of those managers…look at Jack Grealish, he put an arm around him, gave him confidence, they are the type of things players love and Lee has done that. He has been amazing for us. Whatever happens, happens but we are all enjoying this journey at the minute.”