In a sci-fi setting, I was told it was important to follow scientific principles to some extent.
This isn't quite right. There is no universal definition of science-fiction, and the border with fantasy, if there is one, is blurry at best. Generally, what distinguishes sci-fi from fantasy is the use of technology and science vs magic and mysticism, but then you reach a point like Star Wars that integrates elements of both sci-fi and fantasy, and it really doesn't matter if it's one, the other, an hybrid, both, or neither.
I was told it's essential to explain how they function and how they operate.
That's patently wrong, or perhaps a misunderstanding.
Think about The Empire Strikes Back. Why doesn't the hypderdrive work? Mechanical failure? Electronics? Fuel impurity? Overheating? Faulty wiring? We don't know, and it's not important to the story. It doesn't work, and forces the heroes to limp to Bespin, escaping a bunch of TIE fighters through an impossibly dense asteroid field. That's what's important.
We're never told how the hyperdrive works in the movies, or why it occasionally doesn't. We're shown what it does, how the stars stretch when you engage it, and that's the iconic image you remember, that's Star Wars.
You, the author, should know the rules of your technology. You need an hyperdrive to go into hyperspace. That's a simple rule. If you want, you can dig deeper. Power, fuel, physics, etc. Or you can leave it at the bare minimum, just mention there's a device that makes your ship go real fast, or that there's a device that makes your ship not go real fast because it doesn't work currently.
The only requirement is your rules are consistent with each other and you stick to them.
You, the author, should then consider your rules and your story beats, and think about where they conflict (if at all), and whether you'll resolve it by changing the rules or changing the story. Then think about what new conflicts that creates, and repeat until you're satisfied you can make a first draft.
Then comes storytelling, which is ironically where you proverbially show rather than tell.
It's perfectly valid to just describe actions and effects without explaining how they're produced, to show how a technology works simply by describing what the observers see or feel, establishing some limitations through plot where relevant, and leaving the details largely unexplained.
It would be perfectly valid to drill down to explore the purpose of every nut and bolt, to explain the science and the equations, show how every piece interacts with the others, but that sounds like the story you don't want to tell. So just don't.
Is there some way you can do this, especially in the context where you have fantasy mixed with sci-fi, and which requires you to clearly state what's possible with magic and what's possible with technology?
I can tell you what I'd do.
I don't know how my technology works. I have some rules about what goes in and what comes out, what happens in-between might as well be magic (and sometimes is). I have a rule about heat as a limiting factor, and another about the precision of calculation as another limiting factor.
I don't explain any of it though. For travel, I explain that there's a bright flash and the ship vanishes. And from the point of view of the ship, there's a bright flash and everything else disappears. I'm not going to talk about heat sinks and heat management because it's not relevant to the plot. The plot is about the experience of the characters, not the machinery.
But, because I know about the heat rule, I can mention the warmness of the engine bay for flavour, or describe a glowing-red piece of machinery when setting a scene. I won't bother with anything more detailed because that's just running the risk of someone pointing out that, um actually, that's not how physics work.