Parnaby was substituted just 21 minutes into the Third Round tie at The City Ground with a recurrence of a back problem whilst Carsley sustained a leg injury after catching his studs in the turf and was replaced 39 minutes into the 0-0 draw.
"The two injuries were disastrous for us and it shows the fragility of the squad," Blues boss Alex McLeish told Sky Sports after the match.
"Stuart had a recurring back problem. It ceased up and his moving was restricted. He was clearly in distress and we had to get him off.
"Carsley caught his studs in the turf. We are concerned about that one and we won't really have an idea about how bad it is until he is scanned on Monday morning.