Manchester United evoked memories of their famous 1999 triumph in Turin by beating Juventus 2-1 in their Champions League group clash at the same venue last night.
After falling behind to a spectacular Cristiano Ronaldo strike, United hit back in the last five minutes of the game through Juan Mata and and own goal by Alex Sandro.
While he missed the first game through injury, Fellaini made an 11-minute cameo and changed the course of the game with his aerial prowess.
But Allegri thinks Fellaini’s introduction to the game was the turning point.
“In the first game, they didn’t have Fellaini and we used his absence to our advantage,” Allegri said.
“Tonight, he played and his physical presence was immediately felt.
“He controlled some high balls, although sometimes we were good at playing the ball on the ground.
“Conceding those free-kicks was our greatest mistake. That happened and we paid the price.
“We’ll have to learn from that.”
Mourinho, meanwhile, was delighted with his side’s display.
He said: “A point or three would have changed little for Juventus, but three points makes a big difference to us.
“It is a big victory for us, not just because we needed the points but because it was away from home against an amazing team.
“They are a fantastic team with an amazing record at home.
“We had to come and not feel inferior.
“They have more potential than us. Everybody knows their ambitions.”