On-loan Finland international midfielder Tainio cannot play as he is cup-tied having played, and scored, for his parent club Sunderland in their 4-1 away win against Norwich City in the second round of the competition.
Full-back Carr is nursing a thigh injury which he aggravated in the away win at Hull City last weekend and so misses the trip for the third round tie at The Stadium of Light tonight (Tuesday).
Because of manager Alex McLeish's lack of numbers through injury, 17-year-old defender Dan Preston has been given a first-team squad number and could be named amongst the substitutes for the game against former Blues boss Steve Bruce's side.
For a detailed head-to-head between the two sides, click here