The Rossoneri go into their Champions League Group H match against the Spanish giants at the San Siro looking to maintain their unbeaten form in Europe.
Milan beat Celtic 2-0 before holding Ajax to a 1-1 draw in Holland last time out.
They lie second in the pool, two points adrift of group leaders Barca and three clear of Ajax.
"Tomorrow's match is important for everyone but especially for the standings," Allegri said on www.acmilan.com.
"It's always a fascinating game to play against them, it's a game of the highest level in Europe.
"They remain the strongest team in the world."
Barca won the Champions League for the fourth time in the 2010-11 season and reached the semi-finals last season.
"We will have to take a positive result to increase our chances of progressing from the group," Allegri said.
"We will need 90 minutes of great patience, making sure we give them few chances."
The hosts go into the match on the back of Saturday's 1-0 triumph over Udinese that lifted the Rossoneri to eighth in Serie A.
Milan won 2-0 in the first leg of their Champions League last-16 tie back in February before falling 4-0 at the Nou Camp.
"We need to play as a team," Allegri said. "We have to repeat the same game that we played in February from a tactical point of view.
"If we don't play as a team we will lose."
Allegri is hoping the team's top scorer Mario Balotelli, who missed Saturday's match with a muscular injury, will make a return.
"Balotelli is much better and we will evaluate his condition in training today," Allegri said. "We will see if he will feature against Barcelona."
Barca travel to Milan at full strength with only left-back Jordi Alba unavailable through injury.
Lionel Messi, Gerard Pique, Dani Alves and Alexis Sanchez returning to the starting line-up having been rested in Saturday's goalless result at Osasuna.
The outcome halted Barca's perfect start to the campaign and saw their lead at the top of the Primera Liga cut to one point with nearest rivals Atletico Madrid.
"With the chances that we had, we should have won," Barca coach Gerardo Martino said.
"But I'm not worried because I didn't see my team take a step back in terms of performance."
Barca have shown no signs of weakness so far in Europe, scoring five goals while keeping a clean sheet in their opening two games against Ajax and at Celtic.
The game at the San Siro will be officiated by Felix Brych, who gave Bayer Leverkusen a ghost goal in Friday's 2-1 victory over Hoffenheim in the Bundesliga.
Brych awarded a goal when Stefan Kiessling's header landed in the back of the net via the side netting for Leverkusen.