The Blues fought back from 3-0 down but the damage was done in what Clark labelled a "woeful" first half when the visitors scored all three of their goals.
Birmingham had looked impressive in beating Crystal Palace on Good Friday and Clark cut a frustrated figure afterwards.
"Quite simply, without the ball in the first half we were rubbish, with it we were decent," Clark said.
"With it in the second half we were decent again and without it we were good. But in the first half we were woeful.
"Three or four players weren't at it and you can't have that. With the ball, you can have three or four players maybe not having a great day but without it, you have to have 11 putting a shift in.
"I think we got a little bit caught up and excited about what happened on Friday, thinking we could just turn up and play our football, forgetting you've got to win the battles.
"It's a very frustrating day for us when you think if we'd got three points we could have gone eighth in the table."