The 'burying part' isn't something I'd consider a key element at all. It's just the lazy man's way of keeping cuttings viable until it's time for them to root. You could do the same thing by burying them in damp sand until spring, but people have tried that in their refrigerator and run into problems. I use that method on a lot of hardwood cuttings. I've done it with apple, pear, maple, hornbeam, zelcova, elm, Jap snowbell, and probably others I don't immediately remember. It's just easy and relatively foolproof, even if it doesn't come with claims of >100% success.
Perlite is an excellent medium for rooting cuttings. One of the problems you might have encountered is a too small particle size. Coarse perlite is best, and if you can't find it, screening out the fines is a big plus. You don't want the cutting end to be in water - it needs to be able to exchange gasses freely.
If I was starting cuttings in a more conventional way, I would start with a layer of something very coarse. In this case, it's a mix of Haydite (like crushed brick) & extra coarse crushed granite.

Then, I would set the cutting on top of the coarse mix or nestle it into the coarse material a half inch or so.

Then, I would mix just a little of the finer material with the coarse so the transition in size doesn't cause water to perch in the finer medium. I did that here, even if you can't tell. It wasn't necessary because the material on top is the gritty mix and the water wouldn't have perched, but for those using fine material, it's an important step. If I just added potting soil on top of the large particles, water would perch in the potting soil. After I added a little of the fine/coarse mix, I would fill enough to cover about 3 nodes with the finer material. NOTE, that what I call finer material is still VERY coarse in relation to potting soils.

The only thing I would have done differently if the cutting was important to me would be excluding the bark from the gritty mix. Even though I've never had a problem rooting in the gritty mix, I'm sure there are rot pathogens on/in the bark, just as there are in potting soils; except there are probably far greater populations in potting soils than on the bark.
Remember that cuttings need plenty of oxygen to metabolize the energy stored in the cutting. W/o oxygen, your cuttings will fail just as surely as if they lacked water, so think airy and damp - not rich, black, and wet.
Al