Wayne Rooney is expected to be fit for the midweek clash at Newcastle after missing the shock defeat to Blackburn.
The Reds' leading goalscorer started on the bench against Wigan and watched on from an executive box as Rovers condemned United to a second home defeat of the season.
"Wayne hasn't trained well this week, he's missed a few days and we're hoping that he trains today, tomorrow and, by Wednesday, he should be okay. It's little strains here and there."
At least the early signs are that no fresh injuries were sustained in the 3-2 loss and Anderson made an earlier-than-expected return from his lay-off as a substitute.
"It's too early to say," the manager admitted, when asked about any new problems. "There'll be little bumps and bruises but nothing more than that.
"This is the crucial time of the season. We have Newcastle away on Wednesday and obviously we want to make sure we come back with a proper result."
Sir Alex was speaking to ESPN and MUTV.