How much wort should be left in the brew pot?

If you're not comfortable with the strainer approach (or maybe don't have a sanitised one to hand) and wish to continue with the syphon, could the whirl-pooling technique work here? Stirring the brew pot quickly until a whirlpool effect is created. The heavier elements of the break and other ingredients will gather in the centre of the pot allowing you to syphon nearly all of the wort from closer to the side of the pot.

I believe it's a good technique for extract brewing, but having never tried a partial mash I'm not certain if there may be too many other elements to get a positive effect from this technique.

Another easy solution is to use a muslin bag during your boil. Homebrew shops sells them in bulk for under a dollar each. They are like pantyhose and stretch a lot. Stick it in your kettle and clip/tie an end of the bag to either handle. You'll have the bag stretched across the middle of the kettle with the top of the bag open. Whenever you make hop additions, dump them into the bag.

Once your boil is done, just untie the bag and lift it out - the majority of the hop material will come out with it. Hold the bag and let the wort drain from it for a few seconds. Some people say don't squeeze the bag or you'll release bitter compounds. I say don't squeeze the bag because it's really hot and you'll burn yourself and it's not worth it for a half a cup of wort.

I've used these bags when they're included with extract kits and they work very well. They're not reusable but are compostable. There's a small amount of fine hop debris left at the bottom of the kettle, but it's insignificant and can go into the fermenter.

I'd also suggest not siphoning the wort - pour it into your fermenter to get as much yield as possible. Pouring it back and forth between the fermenter and kettle a few times helps oxygenate the wort if you don't have another means of doing so.

The strategy for getting the most wort into the fermenter is to dump it all in. Everything, hops and everything. I don't scrape the stickies off the wall of the pot, but I tip the whole thing into the fermenter.

I generally aim for none wort to be left in the pot. It will make good beer.

If you're not comfortable with that, the strainer idea is fantastic too.

Although we need more information to be more specific, the general answer to "how much wort should be left behind" is "as little as possible". One thing you can do is pour the wort through a sanitized strainer and press the hops with a sanitized spoon to extract the wort in them. Also, once the wort is cooled down, you can simply pour it through a strainer into your fermenter. The strainer will stop the hops, and the rest of the trub that makes it through will not only not harm your beer, indications are that it can be beneficial. The reason why your gravity was low will have to wait til we know more about what and how you brewed.