The 1-0 victory over Chievo was sealed in stoppages by a Clarence Seedorf screamer, but only after Beckham, on-loan from LA Galaxy, had limped off with a ruptured Achilles tendon.
"Beckham's injury makes us all feel badly, as he is such a nice lad," sighed the Milan boss.
"The goal so late to put us within a point of the leaders was wonderful, but we cannot celebrate entirely.
"He already told me when he left the pitch that it was a serious injury. When the tendon breaks, everything comes away and the muscle starts to rise. I felt great pity for him."