Despite initial hopes that Davies would be fit to play in the Griffin Park fixture, the defender wasn't risked for the game after still feeling a problem in his calf during training this Friday.
City also decided to err on the side of caution with James Hanson after the striker aggravated a slight groin injury the same day.
Parkinson said: "Andrew had an injection in his back on Tuesday to help with the neural problem that has been causing the issue in his calf.
"He has had this before and normally after two days the problem has been resolved but he came in on Friday and there was still an element of tightness in the calf.
"As a result, we decided not to risk Andrew for this one.
"James' situation is a frustrating one. We'd trained all week working on how we were going to play today (Saturday) and he was obviously going to be a key part of that.
"James had a groin problem last weekend but trained all this week. Unfortunately though, he's felt it again in the warm-up for training on Friday.
"Again, like Andrew, we decided it was best to leave him out for this one.
"It is not a serious injury though and hopefully he'll be back sooner rather than later."