By ESPNSTAR.com staff
Andrea Costa scored the only goal of the game in the 58th minute to hand the visitors a winning return to Italy's top flight and condemn their opponents to defeat in their opening game of the campaign.
But despite watching title rivals Juventus, Inter Milan and Napoli all pick up victories over the weekend, Allegri refused to get critical over his side's display.
"We shouldn't get discouraged," he said on the club's official website. "We have to improve and bit by bit we will.
"We have all the right pieces to do well so we can't get discouraged and drop our heads. I know there's not much conviction around this team but the team needs enthusiasm and needs to feel supported."
Allegri also defended his decision not to start with new siging Giampaolo Pazzini, who signed for the club earlier in the week in a move which also saw Antonio Cassano join Inter Milan.
"We knew things could be difficult in the first half because we didn't really have a reference point up front," he added. "But I still didn't want to risk Pazzini starting the game because he hasn't started a game for a long time.
"In the second half, it seemed like the ice had melted and the team played with more courage.
"I'm disappointed because the players didn't deserve to lose."
Milan will be looking to get back to winning ways next weekend then they take on Bologna.