Hancox suffered a broken hand after he was pushed over advertising hoardings against Ipswich Town, and Clark has revealed that the 19-year-old will not return until next season.
The 40-year-old told the Birmingham Mail: "It's a shame Mitchell is missing because I was considering having a look at something I'd like to do in terms of a different formation for next season. But Mitchell being out, that's knocked that one on the head for me.
"He keeps badgering me to say he can play and the doctor has said to me that if it was a playoff final or if it was a game like Hull or Watford have got Saturday, he could play. But if he was to land on it again awkwardly, it could go into the joint where the two broken bones are and have serious repercussions.
"I know Mitchell doesn't do anything by halves so there's a great chance that he could do something serious if he played."
The full-back has made 19 appearances for the Blues this season.