Tigers debutant George Boyd scored two goals, Gedo also struck twice and Robert Koren found the target.
Birmingham scored late consolations through Peter Lovenkrands and Chris Burke but errors were plentiful in a sloppy Blues display.
"That's what I have said to them. Let me be down in the dumps on the bus journey home, let me analyse this stuff," Clark said.
"They just have to come in tomorrow (Sunday), dust themselves down and be ready to go (against Blackpool) on Tuesday.
"It is a tough place to come and when you are 30 seconds in and 1-0 down to quite a simple goal it is a tough one.
"From there it went from bad to worse and we were 3-0 down in half an hour. They were not great goals from our point of view - awful in fact.
"The first two are just down-the-middle goals, basic defending. We knew we would come under the cosh against them, they play high tempo, I don't think it was down to our system or tactics."
- Sports & Recreation
- Peter Lovenkrands
- Robert Koren