A match which historically would pit two of football's superpowers against each other takes place at the Nou Camp with the sides no longer on a level playing field following the decline of Italian football.
Milan head to Catalonia as Serie A champions but Allegri concedes they will be underdogs against the side recognised as the best in the world at present.
"We're ready to play this game, a game of great prestige and the first in the Champions League this season," he told reporters.
"We're going to try to make a good start and be balanced in defence and attack. Right now, they are the team playing the best football, they have the highest quality - both individually and as a team - but we have our own quality, we're a good team.
"We're AC Milan, so we must play with courage. In football, you can never take anything for granted.
"There will be a lot of attention on the match and we must have great respect for Barcelona. But we have qualities to make it a good football game.
"We'll go with peace of mind. Tuesday is not a final, it's the first game of the round. It's against a team who have recently won a lot but our goal is to go through."
Asked about Zlatan Ibrahimovic's return to the Nou Camp following his bittersweet spell in 2009-10, Allegri said: "He's proved himself and he's proving he can be a champion on the big stage."
Allegri confirmed he will make changes from the side which drew 2-2 with Lazio in Friday's Serie A opener and will choose between Antonio Cassano and Alexandre Pato to partner Ibrahimovic up front.
Makeshift Barcelona defender Sergio Busquets has urged his Barcelona team-mates to use Tuesday's match to bounce back from Saturday's league disappointment.
Barca let a 2-0 lead slip to draw 2-2 with Real Sociedad in their second Primera Division game of the season at the weekend, with holding midfielder Busquets operating in central defence at the Anoeta.
He admitted: "Morale is not the best today but we'll give a reaction.
"Milan is another game, another competition, and we'll go for it. With the help and support of our fans we'll make it a great night in the Champions League.
"Milan have great players, especially up front. Ibrahimovic, Pato, Robinho and Cassano are very dangerous and we'll have to keep an eye on them."
Barca boss Pep Guardiola is still without first-choice central defensive pair Carles Puyol and Gerard Pique while forward Alexis Sanchez is out for eight weeks with a hamstring tear.