The Chelsea player scored in Tuesday's 3-1 friendly win over Germany in Sheffield.
Folarin Balogun and Cole Palmer also netted at Bramall Lane as the Young Lions made it successive wins after last week's 2-0 victory in Italy.
Gallagher, who has four senior caps, dropped back to the Under-21 fold this month and with boss Southgate naming his World Cup squad in October, Carsley has been impressed with the 22-year-old.
"It's testament to Conor with the way he has approached this camp," Carsley said. "No sign of any disappointment or problems. He has been really positive, trained really well. His application has been great.
"We'll focus more on Conor because he's played in the seniors, but they all need to keep pushing themselves and putting themselves in the window.
"The way you do that is playing well for the 21s and carrying on your form at the clubs."
England went behind 10 minutes before the break when Felix Nmecha headed in from six yards but, after James Garner hit the crossbar, Balogun levelled after 41 minutes.
Gallagher put the Young Lions ahead just two minutes into the second half when he fired in Anthony Gordon's cross from close range.
Arsenal's Balogun, on loan at Reims, and Garner went close to a third but it was Manchester City's Palmer who made it 3-1 in stoppage time, running on to Oliver Skipp's pass and finding the bottom corner.
Carsley added: "They have been high quality opposition, but they are friendlies. I expect a totally different intensity playing in the Euros.
"It was a really tough challenge. We spoke about it before, we knew it was going to be difficult against tier one opposition.
"We tried a few things which has given us food for thought, we want to be a bit more unpredictable with systems and the way we press teams. It was a good solid 10 days."