World War I was the first major war in which many people sat up and said, "wait now, technology seems to have made a huge difference here." As with all things in history there are predecessors (the rout of the French in the Franco-Prussian War of 1870 was also attributed in part to Prussian mobilization of rail technology and the connections between Krupp Industries and the Prussian state leading to innovative and devastating artillery advances), but World War I, with its featuring of novel air power (airplanes, Zepplins), sea power (submarines), and of course the ubiquity of heavy artillery, machine guns, gas warfare, and eventually tanks on the Western Front, was seen by many commentators on the whole as a herald of things to come.
What is interesting, though, is that while this lesson was absorbed by many, it did not result in too many "revolutions" in how governments handled science and technology. Most nations still had anemic military research coordination, and almost no coordination between academic work and military work. Only as World War II began to loom did many governments (including the British, the Germans, and the Americans) start to really take seriously the idea that there needed to be far more coordination between scientific and technological development and military services. Those making the argument that there needed to be such coordination stressed that technological revolutions translated into military revolutions, and would thus translate into victory. Vannevar Bush, the former VP of MIT who pushed Roosevelt to establish a succession of organizations to do this coordination, put it this way: "The world is probably going to be ruled by those who know how, in the fullest sense, to apply science, whatever their other attributes may be." (1941) This sums up the mantra of these scientist-administrators very succinctly.
Bush and others of his generation — people who were young scientists and engineers during World War I, and who would enter in positions of high authority by the late 1930s — in many countries pushed for radical reorganization along these lines, and generally got it (to varying degrees of efficiency). These reorganizations led to the rapid technological developments during World War II, which birthed such marvels such as radar, the first digital computers, the proximity fuze, cruise and ballistic missiles, jet airplanes, and, of course, the atomic bomb. These particular stand-outs were just the most spectacular of many technologies that were developed during the war; there were plenty of "more mundane" advancements in areas like chemistry, electronics, physics, and so on, to say nothing of organizational science like Operations Research.
All of the this meant that by the end of World War II, the role of science and technology in determining the fate of nations was probably over-estimated to some degree, to the neglect of things like logistics and resources. And one should be aware that this public change of perception still took several years to be translated into the modern marriage of scientific and governmental power (the National Science Foundation in the US, for example, did not get created until 1950, after all that, and much of what we think of as the full "Cold War science" period did not begin until after the "Sputnik shock" of 1957).
The fact that many of these technologies were developed in secret and then suddenly displayed, fully-formed, probably also contributed to this sense of rapid technological achievement. While, say, the atomic bomb was indeed developed rather rapidly (it went from table-scale science to an industrially-produced superweapon in less than six years, and it went from "decision to make the bomb" to "the use of the bomb" in only 2.5 years), it looks less magical if one knows every step that was taken along the way, instead of "the discovery of fission" (1939) and "two cities destroyed" (1945), which is how it looked from the outside.
Lastly, I would just note that this "awareness" was stoked and encouraged by two fields which were developing and diffusing over the course of the early 20th century. One was science fiction, which had an immense impact on how policymakers and scientists thought about the discoveries of things like nuclear fission, radar, and the use of bombers in war. H.G. Wells in particular captured the imagination of several very high-placed and high-impact people (including, for example, Winston Churchill, who bought the Wellsian vision of technology hook, line, and sinker). And the other force was the development of science journalism as its own field, which was in its early days (and still, arguably, today) populated by a "gee whiz!" style of writing about scientific and technological changes, stoking the idea that the world was going through a new technological age that was going to change everything (and it did change some things, but not everything). One of the pioneers in this new field and style of writing, William Laurence of the New York Times, was "embedded" within the Manhattan Project and co-wrote nearly every press release and news story (largely anonymously) that was released in the first days after the atomic bomb, as an aside.
Anyway — there is always more one can say here. One can follow these threads through many different books, but if one wants to follow them through one prominent development in particular — nuclear technology — there is no better source than Spencer Weart's excellent Nuclear Fear: A History of Images.