Kevin-Prince Boateng's opening goal put the Rossoneri ahead in the first leg of the Champions League last-16 tie and Sulley Muntari's superb second doubled their advantage. Allegri was not getting carried away ahead of the March 12 return at Camp Nou, though, and urged his players to swiftly turn their attention back to Serie A and the tussle with Inter Milan.
"We haven't done anything yet," he said after the game at San Siro. "We have to leave it there now as we have the derby and we have to recharge our batteries immediately. I'm very happy with what the players have done and we should enjoy this and start focusing on the derby."
Allegri had particular praise for Giampaolo Pazzini, selected up front alongside Stephan El Shaarawy in the absence of the cup-tied Mario Balotelli, and was thrilled to have kept a clean sheet against the Primera Division leaders.
"I'm very happy," he said. "It was an extraordinary game from a defensive point of view as we didn't concede anything to Barcelona. We slipped up on a couple of passes but, in the second half, the team did well. They were patient and they found the right moment to strike.
"The players understood what I asked of them and, when you play with that kind of willingness and intensity, you can win against anyone. The team is still growing. It's doing so very quickly. I think it's a team that will do well for years to come."
He added: "Pazzini played an extraordinary game and he's shown that he's a great player at a European level. The team is made up of 25 players and we need balance and to find the right way to play depending on who's on the pitch. You don't need to motivate the players for these kind of games - just give tactical instructions."
Vice-president Adriano Galliani felt the Italian side produced the "perfect" performance, which showed just how far they have come this term.
"We did very well and I have to say that our coach was very, very good in my opinion," he said.
"We played a perfect match. We did well to prevent (Barcelona) from getting inside the box. We did well against them last year as well, though. We can play with Barcelona and that's what I keep saying."
- Sports & Recreation