Losing a war does not automatically disqualify a country from being economically successful. Japan and South Korea were also devastated by war, but are similarly successful.

Also a large factor was all three mentioned countries had a lot of reconstruction dollars and financial investment pumped into them by western nations after the wars ended.

This is more a question of economics then of history. I will give it a shot. The first thing is that you have to understand the for diffrent people, diffrent kinds of success count more. You probebly, as do most people, belive that the wealth the avg individual comands is the most importent thing, people can buy what the want and thus live long and hopefully happy lives.

However this kind of thinking has not always dominated, without going into diffrent kind of idiologys and belive that operated in europe and germany in last century, we can clearly see that for many of these people, it was far more importent that there country had respect, power and influnce. They did not care, if the farmers had growing income expectation. Even if they did care, and one might argue that Hitler did, they belived that the world was a struggle for fix amounts of resources. Clearly if one country is rich, somehow another country must be poorer because of it. This view, I would argue, dominates in much of history.

Adam Smith of course point out, based on his obeservation and insights, that the real richness of a country was the consumtion of its people and not the gold in the goverments tresury. He point out that cooperation based on free trade would increase the wealth for everybody, the world was not some fixed size pie and to get richer you had to take from others.

This is the needed background, to understand how this can happen. As soon as you ride yourself of the thinking that somehow richness is derived from military power, or how much resources a country comands, you can understand this question.

Now lets talk a bit about economic growth. Substainable growth usally happens when you have good institutions, and economics consider stable property rights, rule of law, freedom of trade as good (extrem simplifaction). The driver of growth is the division of laber and innovation, lets talk about them. Increasing division of laber, makes people better at one task and thus imporves overall performance. Innovation is finding some new social or technical way to increase output or quality. When a country is not on the cutting edge of innovation, it can usually grow much faster until it catches up (because they only have to increase divison of laber, not innovate themselfs).

Now germany was bombed to bits, their and montary system was kaput, on the otherhand they had a large population that was relativly smart and unified (no civil war based on religon or idiology). Thanks to the sensible high level institution imposed on the germans, they had institution that economist would call 'good'. Thanks to private and public investment, the needed capital was around to have very fast catch up growth. Looking at countrys like Germany, Japan, South Korea, Hong Kong, Singapur and so on can really show us that 30-50 years with relativly good instiutions can basiclly get you fully catched up.

This happend in west germany (because of 'western' institutions) but did not in eastern germany (because of socialist institutions). Looking back on what I said about growth, divison of laber increased thanks to beeing part of a large western block of nations. Innovation was created befor and during WW2, germany could take advantage of that and catch up on growth, and eventually push the innovation frontier themselfs.

This is of course a very simplified answer, growth theory alone is a huge subject. The even larger subject of devlopment economics is also relevant.

I would also mention that I have importent questions about military power, argubly you don't just need the right institutions, you also need to be able to defend them.

Edit: As for sources, Im not sure what to point to exactly. Wealth of Nation is the relevant starter but any study in growth and development economics will give you much of these information. If you have any specific question, or you want to know more about these theorys, I can give you better sources.

Edit 2: I want to mention the Marshall Plan. I have talked about investment, and the Marshall Plan is part of that. However I feel it sometimes gets to much credit, at the same time germany also had to pay massive amount back. The Marshall Plan can simple not be used as a causel factor, because it effected many places and not aways showed the same effects. It was at best a speed up, not a kick start.

The most importent moment was when Ludwig Erhard (adviser to US military) simple told everybody on a sunday that the nazi price control and rationing system was abolished. The US administrators were not commited enougth to change it back and the people had allready stopped carring and it seamed to work. Economic recovery started and then months later Marshall Plan aid began to arrive. Belgium did also recover quickly even befor Marshall Plan aid arrived.