The Three Lions were victorious away from home in the Nations League B, winning 3-0.
Atletico Madrid midfielder Gallagher, who impressed in midfield alongside Curtis Jones and Jude Bellingham, spoke post-game.
He told BBC Radio 5 Live: "It was a brilliant performance, very professional. We were desperate to give the fans a good performance and a good result and that is what we were able to do, so we're really happy.
"From the first game against Greece at home we knew their threats and I felt like we dealt with them really well tonight. The counter attack, playing into the front and having runners - we stopped that a lot more and limited them."
On his midfield partners, he added: "Top, top players. It was a pleasure for me to play with them in midfield. I felt like we combined well together on and off the ball in a great performance."