Midfielder Carsley suffered ankle ligament ligament damage during the FA Cup tie with Nottingham Forest while full-back Parnaby pulled a back muscle in the goalless draw at the City Ground.
Blues boss Alex McLeish is refusing to put a time-scale on how long the duo will be out of action except to confirm they will not be fit to face the Red Devils.
McLeish said: "Lee and Stuart are both out for Saturday. We've not put a timescale on when they'll be fit again.
"Lee has got an ankle ligament injury and Stuart has pulled a muscle in his back, so we're not sure how long they'll be sidelined for."
Parnaby made a rare start against Forest as regular right-back Stephen Carr was serving a one game ban for incurring five bookings during the current campaign.
But the duo are still considered as important back-up players by McLeish who is continuing to step up his search to bring in new blood during the January transfer window.
Sporting Gijon midfielder Michel is close to finalising a deal to move to St. Andrews while McLeish is understood to have put in a bid - believed to be around £11 million - for Sunderland striker Kenwyne Jones.