Leeds' top scorer Ross McCormack hit the first goal and had a major part in two others as Leeds romped to their biggest home win since a 4-0 eclipse of Shrewsbury in the Capital Cup at the start of last season.
Birmingham's defence was a shambles and it was ruthlessly exposed as giant striker Matt Smith helped himself to two goals and all-action skipper Rodolph Austin was also rewarded with a downward header past overworked Birmingham keeper Darren Randolph.
Crestfallen Clark made no attempt to hide his disappointment.
He said: "I don't do excuses. I do reality. I will never tell anyone what I tell players in the dressing room, but we are all disappointed.
"That is not acceptable to the badge on the front of the jersey.
"We didn't do anything right in the first half and our defending by the whole 11 was very poor.
"Our passing and forward play were very average in the first half, so it was a frustrating afternoon and we got what we deserved."
Teenage central defender Dan Burn, on loan from Fulham, was hauled off at half-time after a nightmare 45 minutes, but Clark said: "The boy has been brilliant for us this season.
"He is only 19, we have some very young players and they will have ups and downs.
"He made a mistake against Bolton in our last match and he has had an indifferent afternoon, as all players do in their careers.
"We will stick with him because he has been a very good player for us and he will be again."