Davies limped off ten minutes into the second period after sustaining damage to his medial ligament in his left knee.
City had been hopeful that Davies' injury wasn't too severe but a visit by the player to the club's Consultant Orthopaedic Surgeon this Thursday morning confirmed that he will be sidelined until into the new calendar year.
Parkinson said: "Steve will be out for 10-12 weeks. The news is a real blow for him and for us.
"We were hoping that it would be better news but Steven has seen Steve Bollen, our knee specialist, this (Thursday) morning and he's decided that it needs to go in a brace.
"It will be similar to Billy Clarke's injury."
There is better news with regards Josh Morris and Billy Clarke, however, as the pair continue to make progress in training this week.
Parkinson added: "Both have trained again and looked fine. That is pleasing for us."