United got back to winning ways in the league with a 3-0 victory over West Ham, but injury to Anderson and news of another setback for Rio Ferdinand came as a blow to the Reds.
Neither player is expected to be fit for Sunday's Carling Cup final against Aston Villa at Wembley.
Anderson was forced off in the first half at Old Trafford on Tuesday after injuring his knee in a challenge. He played on briefly but then signalled he could not longer continue.
Sir Alex said after the game: "We’ve sent him for a scan. Hopefully it’s not serious but it’s not looking great."
News of yet another back problem for Ferdinand is also worrying. The influential centre-back had just completed a four-game domestic ban and had been expected to return alongside Nemanja Vidic against the Hammers, but he pulled out of the game on the morning of the match.
"He got a twinge in his back in training," explained the boss. "He’d been training great, too, with no mishaps at all with his back. But when you get these twinges you can’t take a chance. He won’t be ready for Sunday, so unfortunately for him he’ll miss a couple of games, I think."