Milan twice came from behind at San Siro but eventually lost out to Xavi's winner in a thrilling match between two of the continent's biggest clubs.
The Rossoneri now switch their attentions back to Serie A action with the visit of Chievo on Sunday night, and Allegri believes they need to cut out some of the errors made against the Catalans.
"We came out of the Barcelona game with a good performance, but we cannot be content with that," Allegri said at a pre-match press conference on Saturday.
"It helped our self-esteem and awareness to grow, as we showed we can battle against the top clubs in Europe.
"Against Barcelona and Fiorentina we played well, but we made some mistakes and need to play more as a team."
And the 44-year-old coach is taking nothing for granted against Chievo.
"Chievo must not be underestimated," he warned.
"They defend solidly and are very dangerous on the counter-attack, so it will not be an easy game. Chievo have beaten Fiorentina and Catania, so we have got to give it our all."
A win on Sunday will see Milan move to within a point of league leaders Juventus, who edged out Lazio 1-0 on Saturday.
"We won [the Scudetto] last year and we are favourites," Allegri added.
"But Juventus are also one of the favourites and they showed that with their summer signings.
"Udinese [second with 24 points, one less than Juve] and Lazio [now fourth with 22] have improved as well and are strong."
Kick-off between Milan and Chievo at San Siro is at 20.45CET.
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