The two giants of football are favourites to advance from Group G of the competition which consists of minnows Viktoria Plzen and BATE Borisov.
Looking ahead to the opening clash, Allegri believes his side have what it takes to upset the reigning European champions.
"We have a lot of respect for Barcelona. They play some of the best football, but we shouldn't forget that we have great players too," Allegri was quoted as saying by La Repubblica.
"We have to be very alert at the back and up front. We can't afford to be careless."
The Milan coach went on to hint that striker Antonio Cassano could be dropped from the starting line-up against the Spanish giants.
"Cassano put in a superb performance in the game against Lazio, but Pato is the favourite to start alongside Zlatan Ibrahimovic against Barcelona because of his specific characteristics."