A late, high challenge from Cesar Tarrega on England full-back Tino Livramento sparked a furious scuffle between the teams as both benches cleared.
Spain's Rafa Marin was sent off after the final for his part in it whilst McAtee was shown a yellow.
But the England captain was pleased with his sides' response to the aggression.
After picking up the player of the match award, McAtee told reporters: “I never saw the challenge (on Livramento), I saw the boys start going into it, so always going in to help. It’s part of football, and you just have to stick together as a team.
“It’s a big game, we know that. It’s two big teams in the tournament, so them kicking off, we can’t sit back and just let them do it, we have to give them a bit back, so I am happy with the boys.”
It followed a battling performance from England, where they produced a scintillating 30-minute period to go 2-0 up, before Spain pegged them back with a Javi Guerra penalty.
Spain pushed hard to equalise throughout the second half, but a last-minute spot-kick from Elliott Anderson sealed England's progress.
Carsley, who was involved on the periphery in the brawl, felt his players' passions after full-time did blow over.
He explained: "I think there are better ways to build camaraderie. But I think we had something similar in the final (two years ago).
"Emotions run very high, and in those kinds of scenarios, you don’t want anyone to get sent off, anyone to throw a punch or get themselves in trouble. You try and be as respectful to both sides, but you can see how much it means to the players.
"To represent your country in a quarter-final means a lot. We probably have to give them a bit of leeway.
"Thankfully, it didn’t go over the top, but it’s still not nice to see. We are always trying to fly the flag and encourage younger players, especially to take up football and enjoy the game… but the passion was just a bit much."
Spain's manager, Santiago Denia, also spoke after the game, saying the behaviour of his players did not tarnish their trip.
He said: "You have to know how to win and to lose, and although the behaviour wasn’t right, we have got to congratulate the opponent – they won the game playing well, and we tried to separate them quickly and calm it down because you have to know how to lose. I congratulate the coach Lee as they beat us again."
