The Italian was speaking ahead of his side's Champions League last-16 second leg clash with the Gunners at the Emirates Stadium tonight.
After an impressive 4-0 victory at the San Siro in the first leg, the Serie A giants are almost certain to progress to the quarter-final stages - a result that suggested a significant gulf in class between Milan's established European players, compared to Arsene Wenger's young Arsenal side.
"For me it's impossible to win the title or Champions League without signing big players," Allegri said ahead of Tuesday's clash.
"You will never do it without big players. That goes for Arsenal, Milan or any big club."
However, despite his strong beliefs on the Gunners' weaknesses, the Milan boss will not underestimate the threat the Premier League club will pose, particularly on their own Emirates Stadium patch.
"Despite the 4-0 advantage, the English never give up," Allegri added. "So I'm expecting the team to be even better than in the first leg, because we know how difficult it will be."