Allegri’s side, who take on Arsenal at the San Siro on Wednesday, were eliminated by Tottenham Hotspur in the round of 16 last season, while Manchester United beat the Italian champions at the same stage in 2010.
And goals from Cesc Fàbregas and Emmanuel Adebayor sealed a 2-0 victory for Arsenal in Milan 2008, booking the London side’s place in the quarter-finals.
“We don’t have an inferiority complex against English teams despite the defeats in recent seasons,” he said.
“Last year against Tottenham we made a big mistake in Milan but in the second game we deserved to win and go through. Arsenal are performing well and their attack is very dangerous.”
Thierry Henry, who bagged a hat-trick in Arsenal’s 5-1 win aover Internazionale at the San Siro back in 2003, is expected to play a part in the game before returning to the New York Red Bulls.
And Robin van Persie, the Gunners’ top scorer with 28 goals, will captain Arsène Wenger’s side on Tuesday night in Milan.
“We are aware of Arsenal’s strength,” Allegri said. “They have individual talent and play well as a team.
“The Gunners collectively are more dangerous than the qualities of two great players like Thierry Henry and Robin van Persie.
“We must be careful and we have to perform well in defence because it’s a 180-minute challenge.”
Milan, who have won Europe’s top prize on seven occasions, have not made it past the first knock-out stage since they won the competition in 2007, when they beat Liverpool in the final.
And Allegri, who led i Rossoneri to the Serie A title in his debut season at Milan, is desperate to reach the quarter-finals for the first time in five seasons.
“We will try to qualify for the next round because we want to improve on our last campaign in the Champions League,” Allegri added.
“We must be careful, play well technically and avoid some of the mistakes we have made recently. Conceding a goal at home would be a blow ahead of the second leg in London. We must not concede on the counter-attack.”
• The encounter four years ago, when Milan were the defending champions, was the teams’ first in the Champions League.
• The Gunners have won just three of their last 12 European games on the road, including the play-off victory at Udinese.
• Milan have collected nine yellow cards, the joint lowest total of the teams in the last 16 along with Barcelona.
• Yossi Benayoun’s goal against Olympiakos on matchday six was the Gunners’ 250th in the European Cup.
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