Brazilian midfielder Anderson has been ruled out until February with a knee injury.
Sir Alex revealed the blow at his Friday press conference after the South American has been missing since being substituted in the home win against Otelul Galati.
"It's in the midfield area where we've still got issues with Tom Cleverley and Anderson," stated the boss. "It's not good news about Anderson, we don't think he'll be fit until February.
"He's got this knee injury and we've sent him back to Portugal to see the specialist who operated on his knee last time. That's a bit of a blow, we didn't expect that one. So that's the two midfield players who are going to be missing for a spell now."
The manager insists he still has enough options in the middle of the park - even though injuries have taken their toll in the position this term.
"We're not as bad as people think we are in midfield," he stressed. "Ryan Giggs gives you experience of course, Michael Carrick’s form in the last two games has been outstanding. He had a little bit of a problem with his Achilles earlier on in the season but he’s got over that now and the grounds are softer now of course which helps.
"Darren Fletcher, given the right preparation, is always a very, very good player for us. Getting Tom Cleverley back would be a bonus if we can get him back around Christmas time. It would be a bonus to get him back because he’s such a clever footballer. I think we’re okay, we’ve got a strong squad."
One thing that is certain is Sir Alex won't be rushing into the January transfer market as a consequence. "It's dead easy to say you'll go out and buy players," he warned. "But it's not easy to buy players who are good enough for Manchester United, especially in January.