The Hoops suffered a 2-0 defeat in Milan in September but felt there were positives to take from a game they were unfortunate to lose.
And, with home advantage on their side this time, Mulgrew says confidence is high in the Celtic camp as they aim to keep their last-16 hopes alive against a team who arrive in Glasgow on the back of poor domestic form.
He said: "It gives us a lot of belief. Although they had a couple of players missing that night, we still take massive confidence from that performance.
"We didn't get the result and we were a bit unlucky and didn't take our chances but hopefully we can take that form into the game tomorrow night.
"We know it will be difficult. AC Milan are a good side, a world-class side, so it will be tough.
"But we know the task ahead and we know what we have to do. It's massive, it's a must-win game for us. We are all looking forward to it."
Celtic head into the match boosted by a hard-fought victory over Aberdeen at the weekend, which keeps the champions five points clear at the top of the Scottish Premiership.
Mulgrew - who is likely to play in midfield - said: "It's always good going into a Champions League game on the back of a win.
"Everybody is positive and excited about the game. Although it's a totally different game and a totally different competition, it gives us a boost and we are all up for it."
In contrast, Milan have failed to win in their last five league matches and sit 13th in Serie A, with fans quickly losing patience with coach Massimiliano Allegri and the players.
Mulgrew said: "You just have to look at the world class players they've got in their side to realise how difficult the game is going to be.
"They've got some great players and we've got to match them and do our bit when we've got the ball.
"You would expect Milan to be a bit further up the (Serie A) table but the Champions League is a whole different competition.
"I'm sure they will be up for it and we will need to be prepared to match them."