The AC Milan boss gave me his first interview for an English paper and spoke honestly and bluntly about the gradual decline of the Gunners.
Outspoken Allegri is the hottest coach in Serie A after winning the title in his first season in charge of Milan.
His rampant Rossoneri thrashed Arsenal 4-0 in the Champions League first leg and all-but secured a quarter-final spot.
Sat at the top of a board-room table at the Italian giants' famous Milanello training ground, Allegri defended manager Arsene Wenger but condemned Arsenal's policy of cashing in on their stars.
By doing that, Allegri argued, Arsenal's message to players and fans is that they lack ambition.
Allegri told me: "For me it's impossible to win the title or Champions League without signing big players.
"You will never do it without big players. That goes for Arsenal, Milan or any big club. You must buy big.
"I have a strong team but in that I have three big players, bringing experience, character, technical ability and leadership. You need leaders.
"For me in every team there are two leaders. One technical and tactical leader and one with character.
"In Milan our technical leader is Zlatan Ibrahimovic. In terms of character, until last year, it was Rino Gattuso. Now Mark Van Bommel or Thiago Silva."
Allegri took charge 18 months ago with a brief to restore the Italian giants as one of Europe's powerhouses.
Milan signed Robinho, Ibra, Kevin-Prince Boateng and Antonio Cassano among others and Allegri delivered instant success, winning their first Serie A since 2004.
Boateng told SunSport before the first leg Arsenal are 'either brilliant or don't know what they're doing'.
But Allegri said: "I don't agree because Arsenal have a big coach. They know every time what they have to do on the pitch. It depends on their rivals as well.
"It's not fair to criticise Wenger so much and it is not right, because every year Arsenal sell one big player or two big players and the team still manage to play well and finish in the top four.
"But it's also true that if they want to win trophies they have to keep their best players. And make two or three big signings.
"If somebody told me this summer we have to sell Zlatan and Prince I would say no. No. Noooo..."
Allegri laughed and joined his hands in mock prayer.
In 2007, star Thierry Henry left Arsenal for Barcelona. Without Henry Arsenal still beat Milan at the San Siro and knocked them out of the competition four years ago.
But the following summer Arsenal lost Mathieu Flamini to AC Milan on a free and Alexander Hleb to Barca.
A year on Emmanuel Adebayor and Kolo Toure joined Manchester City.
After managing to hold on to wantaway Cesc Fabregas in 2010 they still sold the Catalan star to Barca as well as Samir Nasri to City last summer. Allegri's take on Arsenal's decline is simple and based on common sense.
The Milan boss added: "If you sell your big players obviously the other players are also affected mentally.
"Psychologically. For this thing the club is also very important. The club sends the important message to the fans and the players.
"If in the summer Milan sells our big players the message the players and the fans will receive is that the club lack ambition." Allegri continued: "When you start to build the team, the big players MUST stay. Three, four or five years. You need three or four years to win the Champions League.
"My plan is to win the Champions League with Milan in the next two years.
"If we are lucky we can make the final this year but Real Madrid and Barcelona are a step above everyone.
"Though if we face them in one game, anything can happen."
The Milan boss agreed with Wenger that Arsenal have only two to five per cent chance to hit five goals and go through on Tuesday.
But he warned Arsenal can score heavily as they hit seven past Blackburn and five past Tottenham in their last two Emirates showings.
Their Saturday win at Liverpool was a big boost too. Allegri added: "It is possible! Anything can happen. If they score a goal in the first minute and one early in the second half for example then they have 40-45 minutes to score two."
But can THIS Arsenal do it
He added: "Well they did it against Tottenham!
"If we make mistakes and are not focused of course they can cause problems.
"It's normal what Wenger has said and I agree their chances are about five per cent because we have a great result in our favour.
"But it is important to play the game with the same mentality as we did in the first leg.
"Arsenal have very good young players and Robin van Persie can make the difference. But I would not change any of my players for any of Arsenal's players. Nobody.
"Because I believe in my squad above anything else."
(一个慢牛)