Rice scored England's first goal since the departure of long-serving manager Gareth Southgate when the Arsenal midfielder netted in the first half of the Nations League opener in Dublin.
Carsley, who led England's Under-21s to European Championship glory last year, is in charge on a temporary basis while the Football Association search for a successor to Southgate.
Southgate quit after England's Euro 2024 final loss to Spain in July, a painful conclusion to a campaign that featured scathing criticism of his conservative tactics and failure to get the best out of a world-class squad.
In contrast to Southgate's caution throughout an eight-year reign that included two Euro final defeats, former Ireland midfielder Carsley revealed his desire to play with the handbrake off as England dominated in a stylish first half.
Statistics showed they created six 'big chances' -- more than in any of their matches at Euro 2024 -- and had more shots (16) than in all but one of their games in Germany.
Rice symbolised the freedom provided by 'Carsball' as he was allowed to advance far further forward than at the Euros, where he served as a defensive midfielder.
Let off the leash, Rice netted the opener and then laid on Jack Grealish's goal before the break with an astute pass.
"All I know is that from us, from the set of lads, we've been so impressed with him this week. He's been so refreshing," Rice said of Carsley's credentials to get the job on a permanent basis.
"His meetings have been top, really to the point, and the way we play and train is really different so I think all the lads are really happy with him.
"Obviously, we had such an amazing time with Gareth. Some of the best memories that we probably could ever imagine. The only thing that was missing there was, obviously, we didn't win a trophy.
"But with Lee now, I think he's adapted so well to the job. He's given a lot of lads a lot of confidence to go and play."
'Personality and confidence'
Carsley's willingness to encourage England to build possession from the back was clear from keeper Jordan Pickford kicking long only 18.5 percent of the time, as opposed to 49 percent at the Euros.
Like Rice, Manchester City winger Grealish enjoyed more license to entertain under Carsley.
Grealish was left out of the Euro squad, with Southgate unconvinced by the forward's freelancing outside the team pattern of play.
But Carsley gave Grealish the number 10 role behind Harry Kane and he repaid the manager's faith with a dynamic display.
"Look at Jack today. I think Jack's best when he's got an arm around him and he's told how good he is," Rice said.
"I think Lee's done that this week and Jack went out there, and when Jack's playing with personality and confidence he's one of the best players in the world."
Newcastle winger Anthony Gordon, who made only one substitute appearance at the Euros, was also given free rein to attack by Carsley with impressive results.
"The expression, the freedom to express yourself was missing from Euro 2024," Gordon said of the change.
"We controlled games but we weren't dynamic. We weren't relentless. We lacked dynamism and excitement."
Birmingham-born Carsley's decision not to sing 'God save the King' before kick-off provoked criticism from England's more patriotic fans.
But if the 50-year-old can coax another eye-catching performance from England in Tuesday's Nations League tie against Finland at Wembley, the anthem issue will be forgotten.
Newcastle's Eddie Howe remains the bookmakers' favourite for the England job, but Carsley's stock is rising.
