The Rossoneri coach is trying to turn up the heat on the Bianconeri, who allowed the reigning champions right back into the Scudetto race with a draw at home to Lecce
The Bianconeri currently sit one point above the Rossoneri ahead of their meeting with Cagliari on Sunday. Milan, meanwhile, meet Inter at the same time.
The reigning champions simply have to win the Derby della Madonnina in order to keep their Scudetto hopes alive but Allegri believes his players will be play with a freedom that their title rivals cannot.
"There’s no need for excessive levels of tension because the team with something to lose are Juventus," the 44-year-old coach reasoned.
“But the players have to get the right mindset for the game and we have to get there as calm as possible.
"We’ll have to play with enthusiasm and courage knowing that we have the ability to win and then we’ll see what the other team does."
Rossoneri fans will be hoping that Sunday unfolds in much the same manner as Wednesday, with word having reached them during the closing stages of their victory over Atalanta that Lecce had snatched a late equaliser against Juve in Turin.
Allegri, though, feels that the celebrations in the stands will be even more enthusiastic if positive news arrives from Trieste.
“These are different days to the days before Wednesday as now we’re only a single point off them," he pointed out.
"We have the derby ahead of us, which is always a special game, and we have the chance to get past Juventus as well, even if their destiny is still in their own hands.
"After losing top spot, there was disappointment and bitterness because we could see the league getting away from us while Juventus is achieving something important.
"Conte is doing a great job, he’s on top of the table and he’s up against Milan. At the moment they’re favorites and I send him my compliments regardless of how the season ends.”
Allegri is bidding for his second successive Scudetto after leading Milan to the title last summer, just a year after his arrival from Cagliari.