Blues have been in talks with Caddis' parent club Swindon following the right-back's impressive loan stint at St Andrew's this season.
However, those negotiations have collapsed and Clark believes any deal is now dead.
He told the Birmingham Mail: "The only way it can be resurrected - which I don't think Swindon will do - is if they make him available as a free transfer.
"It's a blow for me and a huge blow for Paul, who has loved it at the football club. He really settled with his young family and I have been delighted with his performances.
"We are all disappointed and I'm more disappointed for the lad as I know how much he was enjoying it with us and how he was looking forward to joining us permanently.
"But we are where we are. I have been as transparent as I can be with the supporters, I have told them the position, and we have to move on."
Caddis, who has a year remaining on his contract at Swindon, made his debut for Birmingham in September following a deal that took Adam Rooney in the opposite direction.