But although the signing of former United star Cristiano Ronaldo has boosted Juve's chances of a first Champions League crown since 1996, Allegri feels Barca are the frontrunners.
"This year the favourite for the Champions League is Barcelona, but we are amongst the top four," Allegri told a news conference ahead of Saturday's home game against Cagliari.
"Tomorrow, we have to win and winning is never an easy thing as we saw against Empoli.
"Our opponents have their objectives and they will give their all against us. We can't afford to drop any points.
"You have to focus more in Serie A, because in the Champions League focusing happens automatically as there are not as many matches and they are all tough. Therefore we must always show respect and concentration.
"Cagliari are a difficult opponent. They are the team that has covered the most ground in the league and are dangerous in the box. We have to win and prepare ourselves for Wednesday's game.
"Cagliari are a very quick team and [Leonardo] Pavoletti up top is very strong on set-pieces. If you concede more than 30 goals then you won't be winning the title, so tomorrow we have to keep a clean sheet."
Mario Mandzukic and Sami Khedira are available to face Cagliari, but Allegri will be without key defender Giorgio Chiellini and winger Federico Bernardeschi.
"Tomorrow, Chiellini and Bernardeschi are both out, whilst Khedira and Mandzukic are back in the group," Allegri confirmed. "Bernardeschi returned from national team duty with a leg problem but I kept playing him and then he didn't play for this reason. Now I've decided to give him a rest and let him recover completely.
"In the midfield tomorrow both Miralem Pjanic and Blaise Matuidi will play. For the third option I'll choose between Rodrigo Bentancur, Juan Cuadrado and Sami Khedira. In defence there will be Joao Cancelo and Leonardo Bonucci, and I'll choose between Mattia De Sciglio and Alex Sandro on the left.
"Up front Cristiano will play and then I'll have to choose who will play with him between Paulo Dybala, Mario Mandzukic and Douglas Costa. In goal Wojciech Szczesny plays, although Mattia Perin is doing well and he will get more game time soon."