England are second in Group B2 behind Greece with nine points from four games after Jack Grealish, Trent Alexander-Arnold and Declan Rice scored at Helsinki Olympic Stadium on the heels of Thursday's humbling 2-1 home loss to the Greeks.
While Carsley was pleased with his team's response after their shambolic defeat at Wembley - his first setback since Gareth Southgate stood down as manager - he remained tight-lipped when pressed again on his job aspirations.
"This job deserves a world-class coach who has won trophies and I am still on the path to that," said Carsley, who had managed England's under-21s since 2021 before stepping in as interim boss for the senior side.
"I keep saying the same thing. My remit was six games and I'm happy with that," he added.
"This is a privileged position. I'm really enjoying it but I didn't enjoy the last two days. I'm not used to losing in an England team, I don't take losing well.
"People are always going to try and put their chips on one side. I'm in the middle."
However, Grealish and Rice had kind words for their stand-in boss after Sunday's victory.
"It's been so refreshing, he's been so honest, so upfront, just says to go out and play with freedom, and I think you can see us lads, we're playing really well out there and, yeah, really enjoying our time under him," said Rice.
"There's going to be bumps along the way, that's football, it's an up-and-down sport, nothing is ever going to be perfect."
Grealish, who was left out of Southgate's squad for Euro 2024, now has four England goals after his sublime finish from close range put the visitors on the scoreboard in the 18th minute on Sunday - two of the strikes have come under Carsley.
"Whatever happens with the England manager, people will always say negative stuff," Grealish said.
"Before people were crying out for all attacking players to play and it didn't work (on Thursday versus Greece). I don't get it, it can happen in games.
"I love coming here, a top, top manager and I love playing for him."
