Davies was replaced fellow defender Alan Sheehan at the interval at Coventry's Ricoh Arena after banging his arm during an aerial challenge late on in the first period.
City also brought on Mark Yeates for Francois Zoko during the break, with the Irish attacker scoring a well-taken second half free-kick to earn the Bantams a share of the spoils.
Parkinson said: "Andrew bashed his arm and we didn't want to take any chances, especially given it was around the same area where he broke it earlier this season.
"It was in that same sort of area so there was a bit of concern and we wanted to play it safe.
"We're not too sure how bad it is at the moment but Andrew was being bothered by it and there was no reason to take any risks and put him back out there when we had someone of Alan's quality on the bench.
"With Francois, he was a bit unlucky to come off but we just needed to change the shape of the side and get Yeatesy on the pitch. That was it really because I felt Zoko had done a lot of good things."