Zlatan Ibrahimovic and Kevin-Prince Boateng score to lead AC Milan's comeback over rival Inter Milan for an Italian Super Cup win at Beijing.
Milan come back to win the Italian season curtain raiser
"A derby game is always a derby. We really faced difficulties with stamina in the first 30 minutes as players looked tired," Allegri, told a news conference after the season curtain raiser.
"But in the second half, it has turned out to be much better. We did not give any more chances to Inter except Wesley Sneijder."
Gian Piero Gasperini, the new Inter coach, who replaced Leonardo during the close season as the Brazilian became Paris St-Germain sports director, struggled to find positives: "We played very well in the first half."
Milan's first goal came after Clarence Seedorf chested down a cross near the touch line, then knocked it back in for Ibrahimovic to send a diving header into the net. Ibrahimovic had also hit a post with a header against his former club in the first half.
The equaliser was quickly followed by Milan's Alexandre Pato running on to a through ball. His shot hit a post, but Boateng slid to knock in the rebound.
Boateng celebrated with a spinning kung fu kick that delighted the cheering crowds packed into the Olympic stadium.
The venue has proved an unlucky one for Inter. They played in the same fixture at the same stadium two years ago and lost 2-1 to Lazio.
The victory moved Milan one Italian Super Cup clear of Inter and two in front of Juventus.
The Super Cup is the traditional curtain raiser for the Italian season, played between the previous season's Serie A winners (Milan) and Italian Cup victors (Inter).
Three of the next four Super Cups will be played in China to help promote Italian football in Asia.
The new league season starts on August 28 when Milan travel to Allegri's former club Cagliari and Inter host Lecce.
The games are under threat of a strike by the Italian player's association over a long-running disagreement with the league over a collective contract, with two strikes narrowly averted last season.