Ya know .. this one's always bothered me.. well not always.. but since I started reading the SFB stuff
A game or two of Federation and Empire will explain this to you.
The first thing to remember is that nearly half of ever races economy is in their captial hex. (The Federation capital hex includes earth, Vulcan, Rigil, Andoria, and a few more.) Thus a race can lose large stretches of space without their economy becoming totally crippled.
The second factor is off-map area. The Feds are able to send ships directly off-map and look for more resources to exploit, whereas the Klingons (hemmed in on all sides) have a harder time doing this and must lease off-map space from the Lyrans.
The third and perhaps most important factor is economic exhaustion. The longer a race operates on a wartime economy, the less they are able to squeeze out of their provinces. The Klingons have been at war with the Kzinti and Hydrans for years before they invade the Federation. They don't get the quick victory they hope for, and thus they hit economic exhaustion before the Feds.
The Hydrans do make enough ships to drive the Lyrans/ Klinks out of their space, but only after the Klinks/Lyrans have had their fleets decimated in the war with the Feds.
The Romulans enter the war years later than the Feds, but were operating basically on a wartime economy for six years before they enter the war. This was because they had to build a whole new fleet (the hawks) and upgrade two outdated fleets (the kestrels and eagles) before they could launch their invasion.
The Gorn, of course, enter the war last, and have a perfectly healthy economy. Since the Klinks and Roms don't quite force the Feds to sue for an early peace, this turns out to be a bad thing for the Roms. Which escalates into a bad thing for the Klinks. Which is a lucky break for the Kzinti and Hydrans..
-S'Cipio
The Feds are an economic powerhouse, no doubt.