Dave Jones now has to deal with missing Parry, the suspended Stephen McPhail and the injured Willo Flood for the visit of Ipswich Town.
"Parry's a real blow because we didn't expect the scan to show what it did, but it gives others a chance to come in and stake their claim," Jones told BBC Sport Wales.
"He'll probably be out for between four and six weeks, anything less would be a bonus.
"If we can get through the Christmas period and into the January transfer window we'll see if we can bring in the sort of players we want."
Jones is struggling to prepare adequately with training facilities being a problem.
"We've been using Glamorgan University's fields at Treforest, but with the weather in the last three weeks the pitches have become too heavy," said Jones.
"It's been biting us hard, but we knew it was going to happen and I can't control the weather.
"Our new training facilities (at the Vale of Glamorgan Hotel) will be ready in August or September next year, but that doesn't help us now."
The injuries and suspensions along with lack of decent facilities must surely be contributing to the poor form of late.
City face Ipswich on Saturday with a chance of regaining top spot. We'd need Birmingham and Preson to fail as well as City winning.