Despite the Blaugrana heavily dominating possession, with the Serie A side holding firm at the back, before second-half goals from Stephan El Shaarawy and Sulley Muntari sealed a memorable triumph.
Allegri was quick to pass all the praise onto his players, telling reporters: “We won an important game against Barcelona, which I believed in and nobody else did.
“In order to win these games, you need everyone to sacrifice themselves and work hard. We kept Barcelona out of our penalty area and they didn’t have a single real shot on goal.
“The lads played well in defensive terms and didn’t let them near our penalty area. We knew Barcelona kept possession for about 65 per cent of the time, but we had five or six very favourable situations where we got the final pass wrong.
“They didn’t lose heart, even when Barcelona kept possession like that. Perhaps we were lucky with the ricochet on the first goal, but these things happen during a game. My players all deserved this evening, as did the club and the President.”
Despite Milan appearing to have one foot in the quarter-final, Allegri is refusing to rest on his laurels and is already looking to prepare his side for a positive result in the second leg at Camp Nou.
“At the moment this result is not enough to qualify us, so we hope to get a positive result at Camp Nou too,” explained the 45-year-old coach.
“We’re not facing a different Barcelona in Spain, as this is their approach and they always play the same way. We used the ball well, though every now and then we make life difficult for ourselves and that is something we must improve on.
“We can put this result aside now, knowing the second leg will be very difficult and we must try to get another goal with a little more sharpness.
But the Rossoneri boss will first turn his attention for Sunday night’s crucial Serie A clash against Inter in the Derby della Madonnina, with both sides level on points.
“Now we have to think about the derby, which is another important test we must overcome,” said Allegri.
“We need to stay relaxed. We have three days to recharge our batteries and prepare for the derby, I see my team in good shape.”