With the first leg at Old Trafford ending 1-1 last week, AC Milan had their noses ahead when the two teams went at 0-0 into the break in the second leg at the San Siro.
Pogba was introduced to the game at the start of the second half and he scored the winner just a few minutes later to take Manchester United through to the next round.
Brown insisted that apart from his goal, Pogba brought a sense of calmness to the proceedings with his ability to hold the ball and gave Manchester United much needed control in the second half.
He said on MUTV: “Paul coming on was the difference for me.
“Complete calmness, he took his chance and even throughout the game after that, he just controlled it.
“When he had the ball you could see he was calm, he always had control and we sort of played off it.”
The former Manchester United defender pointed out that Pogba exudes calmness for the rest of his team-mates and with his ability to hold the ball he takes the pressure off the rest of the players.
“For me, when Pogba is on the ball everything is calm.
“He knows exactly what he is doing, he is in control of it and it takes a little bit of pressure off the other lads.
“You know he is not going to lose it, he has got the strength to hold people off.
“He takes the ball gradually down the field and you could see the opponents are scared so they drop off and then we have more time to play.
“He did it superbly tonight.”
Pogba is coming back from a two-month injury layoff and it remains to be seen whether Ole Gunnar Solskjaer decides to name him in the starting eleven when Manchester United take on Leicester on Sunday for a place in the FA Cup semi-final.