They crashed out of the competition after a 5-1 aggregate loss to Atletico Madrid, who humbled the Italian giants 4-1 in the last-16 second-leg tie on Tuesday night.
The Gazzetta dello Sport was critical of Balotelli after the Italy international failed to make any impact over both legs: "Balotelli remains switched off.
"Terrible performance by the Rossoneri.
"Kaka goal, Balotelli disaster."
Clarence Seedorf, who took the Milan reins in January following the sacking of coach Massimiliano Allegri, has also come under fire.
Gazzetta's editorial questioned Seedorf's tactics and Balotelli's attitude.
It said: "Balotelli and Seedorf are also under scrutiny.
"Zero Milan, beaten and out of everything."