This is an awkward question but here's an attempt at something useful: the European Christians of the Medieval period became aware (at least by around 1000 CE) that there were societies in the world that could do things technologically that they could not do. They knew that the Islamic world had fantastical machines, for example, that they had no idea how to make. They fetishized reports from abroad regarding these machines and developed a pretty rich iconography about them that somewhat anticipates later discussions of "robots" and "automata."

One of my favorite examples of this are artificial trees decorated with artificial birds that, when air or water was pumped through them, could mimic singing. Reports of these kinds of wonders circulated through the higher stations of the medieval world, and sometimes gifts of this sort were even made to European leaders. In 807, for example, Harun al-Rashid presented the court of Charlemange with an elaborate water clock:

marvelously contrived by mechanical art, on which the course of the twelve hours was marked by a clepsydra, with the right number of little bronze balls, which would fall into a basin when the hour was complete and make it sound. [This clock] also had the same number of horse men, and they would, through twelve windows, come forth at the end of the hours. With the force of their exit they would close the proper number of windows, which had before been open.

So there was a definite sense, at least among the people exposed to these kinds of objects or accounts, that there was a craft beyond them. Note that they didn't necessarily care about that craft — the Franks thought this kind of thing was interesting but not worth serious consideration or emulation.

Which is a separate thing from them saying, "gosh, if only we had a steam engine!" or something like that. I don't think it's too much of a leap to say some of the aforementioned accounts are sort of an equivalent of medieval "science fiction" though it was obviously a very different idiom and genre. The kinds of "imaginative" technologies were less what we would think of as "technology" than what we would think of as "magic" — e.g. inanimate objects becoming alive as golems or monsters, not machines. Whereas in the Islamic world at this point there was definitely a sense that you could create machines that did interesting things. Al-Jazari, in 1206, wrote a Book of Ingenious Mechanical Devices which described a wide manner of purportedly real automata, like mechanical servants who could give you wine. No magic, just gears.

But note that even in the Islamic world there was not a drive to take this approach and couple it to make things of benefit to industry or broader social needs. In both Europe and the Middle East, on the whole, craft work was de-coupled from what we would think of as scientific work for the most part, and while there was at times much emphasis on "practical" knowledge, it was mostly in areas like medicine and maybe navigation, not technology as we have come to define it post-Industrial Revolution. There was more attention to that kind of application in places like China in this period, but while there was always some contact with the West it was much more limited as a result of the geographical distances. Much later, when the Industrial Revolution was in full swing, the Europeans worked to emulate and transform Chinese technologies (block printing, ceramics, etc.), and with great and well-known effect. But that required a lot of other things to happen first, and I am not sure exactly when they first knew about such things.

The definitive study on much of this sort of thing (from which all of the above comes) was published my a friend of mine last year: E.R. Truitt, Medieval Robots: Mechanism, Magic, Nature, and Art (University of Pennsylvania Press, 2015). The hardcopy is rather expensive but it is apparently coming out in paperback soon.