Milan's city rivals Internazionale, at the time led by Jose Mourinho, managed to beat Barcelona over two legs two seasons ago with the help of ultra-cautious tactics but Allegri implied that was not his team's style.
"It's difficult for us to play a match in the style of Mourinho's Inter, they were a more physical side," said Allegri, whose side host the European champions at San Siro in Wednesday's first leg.
"We will face Barcelona with courage, motivation and serenity... We have to try and make as few mistakes as possible and play with an attacking mentality."
Allegri suggested that striker Robinho, who has been out of action for two weeks with an ankle injury, could be fit in time to start the game but said that right-back Ignazio Abate - a key player throughout the season - had been ruled out.
"We will have to evaluate the condition of Robinho, but we also have Maxi Lopez and Stephan El Shaarawy," he said.
"I have my solutions for the defence," he added, referring to the injury to Thiago Silva, the linchpin of the central defence, who limped out of Saturday's win against AS Roma in the first half having been passed fit to play.
"I took a decision," said Allegri. "If he hadn't started and we had played badly, I'd be criticised for that as well."
Forward Zlatan Ibrahimovic was inevitably asked about his relationship with Barcelona coach Pep Guardiola following his acrimonious departure from the Nou Camp 18 months ago.
"Will I extend my hand to Guardiola? I don't know. We've other things to think about. It's not a big problem, I'll do my thing and he'll do his," the Swede said
"There's no time to think about the past."