The Klingon culture has an advantage in this regard because it seems that practically everyone is a warrior of some sort. Klingons despise for-profit business as much as the Federation does, apparently, as it violates their sense of honor. (Of course, this means that the Ferengi Alliance is likely to be the dominant power in the Alpha Quadrant within a century or two.) This, in turn, severely limits the civilian industrial infrastructure.
I'm not even sure if there are such things as Klingon civilians, really. There are Klingon scientists and engineers, sure, but their military seems to revolve around the concept of the citizen-soldier and their culture around the warrior ethic to the point where the most reliable way to earn a promotion is to challange your boss to a duel to the death. They even have codified rules that allow any Klingon to challange the Head of Government to a duel for the position.
Like the Spartans, they pride themselves on being hardcore, so most comforts are anathema to them. They train hard to fight and kill and don't have time for much else.
This is an unfortunate side effect of them being a culture of the hats. Their hat happens to be war and battle. With an entire culture that rejects the very concept of being a civilian, that sees anyone who is unable or unwilling to fight as being disgraced or dishonored, it would make sense that they would lack civilian industrial infrastructure.
The best way to do this would be to set up the Klingon Empire to Mirror Sparta, with all Klingons being citizen-soldiers who are required to train and to serve in the military for a time, while the other infrastructure needs such as farming and manufacturing are taken care of by client races, who have either been conquered or joined the empire voluntarily for protection against even worse races.