Carsley, who had been managing England's Under-21s since 2021, and led them to the European title last year, will oversee two games this month with a view to staying on through the autumn as England search for a full-time successor to Gareth Southgate.
Asked if England's forward-thinking display - albeit against a team ranked 54 places below them - was the mark of "Cars-ball", the former Everton midfielder said this was certainly not the case after just four training sessions together.
"It's definitely not that, it's the players. I'm just lucky that at the minute I'm coaching them," the former Ireland international, who accidentally walked into the wrong dugout at the start of the game, told a press conference.
"The players have got to take a lot of credit the way they took on some of the things we spoke about, moving the ball forward quickly, running forward, trying to get in pockets, I thought they did really well."
Carsley also addressed criticism in some English newspapers over his decision not to sing the national anthem - something he has never done throughout his international career - saying he did not think it made him or anyone else any less committed.
"I was looking forward so much to today, it's the proudest day of my football career," he said, adding that it could not have been scripted better against a team for whom he won 40 caps.
Carsley's players sent some of the praise back the way of their temporary boss, who like Southgate has been installed as a caretaker while also being a candidate for the job.
"It's been really refreshing this week, he's been amazing to work with, his meetings have been top, the way he's worked in training has been really good. I've really enjoyed it and so have all the lads. It's been a fresh start," goalscorer Declan Rice told ITV Sport.