Williams suffered a thigh strain in the defeat at Goodison Park while Thirlwell picked up a calf injury.
Wilkinson said: "From the weekend Paul Thirlwell and Darren Williams have been added to the injury list. At the moment I'm not sure how they will be for the weekend but they must be doubtful.
On a more positive note, midfielder Jason McAteer should return to training next week after being out of action since September and undergoing two hernia operations.
"Jason McAteer should return to training next week and if he is it'll be great news."