The Red Devils blew a chance to put pressure on Manchester City by tentatively taking top spot with a positive result against Blackburn Rovers, as they succumbed to a 3-2 defeat on the day.
Meanwhile, Nemanja Vidic is out for the rest of the season while Jonny Evans, Rio Ferdinand and Chris Smalling are all recovering from their respective injuries.
Sir Alex acknowledges that he has problems in the defensive department, but insists that the Red Devils are not looking to add to their squad.
“Why should you put a sticking plaster on something? We’re quite happy with what we’ve got at the moment,” he told reporters.
“Who is going to sell their best player in January? I don’t see it happening.
“I would like to get one or two out on loan, particularly the young strikers, but at the moment we don’t need to do anything.
“The form of Ryan Giggs and Michael Carrick has been outstanding.
“I’m lucky I’ve got versatile players like Ji-sung Park, Antonio Valencia and Giggs who can play in a variety of positions and give me options.
“The crucial thing, though, is to get our centre-backs back. That’s the only caution I have about my team. Forward-wise and in midfield, we’re OK.”