The Brazilian midfielder pulled up in the cup tie and was given treatment at the side of the pitch before being pulled off at half time and replaced by Wayne Rooney.
But after scans on Monday it turns out that the damage is more serious than first thought with the player having a torn hamstring.
This means Anderson will be missing for the Champions League game against Marseille as he has been sidelined for eight weeks.
The 22 year old had just started to find form after battling back from a cruciate ligament injury.