De Bruyne, who is returning from a fractured eye socket and broken nose, was brought on by Roberto Martinez with his side a goal down in Copenhagen.
De Bruyne duly delivered a masterclass, knitting play together and providing a goal and assist to propel his team into the knockout stages of Euro 2020.
Souness said, "We never mentioned the defenders in the second half, it's as if De Bruyne comes on and everyone grew in stature.
"It's as if, all of a sudden, 'We've got belief about us'. They were a completely different team in the second half, they were rocking from the first minute to the 45th, then you get your top man on and it was like 'He's here, we're gonna be okay'. He influences the game. It's a different level."
Souness added: "It was a game of two halves, the old cliche. But it's de Bruyne, one of the best players in the world coming on. The way he disguises it (his goal), he looks like he's going to pull the trigger it with his first touch. He doesn't - he sends two people to the ground. In no time does he know what's inside him - he's just got a sixth sense.
"People can have the same qualities in terms of abilities, but the special players have a picture in their head that separates them from the rest."