Rhian Brewster’s penalty and Palmer’s excellent goal gave the Young Lions a comfortable 2-0 win over Kosovo to kick off their Euro 2023 qualifying campaign.
Palmer took his chance after Emile Smith Rowe was forced to pull out of the Group G game in Milton Keynes on Tuesday through illness, with Carsley promising to help the forward through his development at City.
He said: “It’s a really tough team to get into and, like a lot of players who play for the top six clubs, it’s very difficult to get game time on the level that they have to.
“The thing we can do with England is to support him as much as we can, we rate him highly, he more than deserved his place in the squad.
“The balance is making sure we try to get his minutes and keep supporting him because he’s a real talent.
“I have been around international football a while now and nine times out of 10 you have players in the squad who, if someone drops out, are more than capable of starting. Cole took his chance.”
They went ahead after just 10 minutes when Brewster converted from the spot for his first Under-21s goal after he was brought down by goalkeeper Leo Besson.
Marc Guehi denied Mark Marleku a leveller after Joe Bursik parried Kreshnik Krasniqi’s drive before the Young Lions doubled their lead.
Palmer collected a loose ball on the right after Conor Gallagher failed to reach Thomas’ cross.
He turned Florian Hoxha, drove into the area and fired past Besson from the angle.
Noni Madueke and Guehi had chances to add to the lead, while Bursik saved from Diamant Berisha during a forgettable second half.
“The effort, professionalism and the way they conducted themselves against a tricky opponent was excellent,” Carsley added, having seen Friday’s friendly in Romania called off after two positive Covid tests in the camp.
“We spoke about getting off to a good start, the new players coming into the team and the responsibility which comes with that. The professionalism the players have shown through the whole camp has been excellent.
“We’ve got Under-19s, 20s and last campaign’s 21s, putting three group of players together so to get a seven-out-of-10 performance is something they can be proud of.”
However, the Young Lions did suffer a late blow when Tottenham midfielder Oliver Skipp limped off late on with a groin problem.
Carsley added: “I saw him on the treatment table with ice on his groin. He said there was a bit of stiffness there. We should know more tomorrow, but Oli’s a robust player. The intensity he plays at, he’s 100 per cent for 90 minutes. He was excellent tonight and he’s going to be an important player for us.”