The Italian side opened the scoring through an exquisite half-volley by Kevin-Prince Boateng, before Robinho doubled the lead with a header.
The Brazilian attacker added a third after the break with a low shot, before Zlatan Ibrahimovic converted a late penalty to compound Gunners fans’ misery.
Arsene Wenger was understandably disappointed with the result.
“It’s very difficult, but what’s more difficult to take was the performance we produced tonight,” he said on Sky Sports.
“Defeat can sometimes happen when you play well, but I felt that defensively and especially offensively we were poor.
“We were in trouble with the same problem, the ball over the top. Slow to read the game and slow to respond. Well beaten in the challenges. Of course it was a big, big problem for us the whole night.
“We were well beaten and never in the game. It was a big shock,” he concluded.
Arsenal will look to bounce back in the FA Cup this weekend, as they take on Sunderland at the Stadium of Light on Saturday.
By Gareth McKnight