Sea anemones can be very particular about the type and size of morsel they will accept. Sometimes there is a total lack of interest, and sometimes you have ingestion followed by the excretion of pseudo-feces: that is to say, the food is ejected, largely undigested, and coated with the anemone's gut-mucus.
Many of the anemones sold in LFS (at least the many that I've seen in CA, IL, NY, TX) are not in prime condition ---and it is understandable that collection, shipping and crowding can take its toll. Even healthy specimens will often refuse food if they have not adjusted to their surroundings.
So here's what you can do:
1. When it's a new introduction like yours, leave it be and wherever it decides to set up shop, make sure it is well lighted.
2. Unless there's clear sign of injury (and in that case why'd you buy it? haha) back off on any antibiotic or prophylactic additives. A significant part of many host anemones' nutrition comes from ingesting the very mucus that coats their oral disc and tentacles, along with any adherent debris and colonizing bacteria and protozoa. You don't want to nuke the mucus clear of the very snacks being trapped or farmed in it.
3. When you do proceed to feed, try very very small portions of very FRESH shrimp or fish --the flavor (chemical cues) will be all the more familiar to the anemone for the freshness. Once they're comfy with the chow, you can try gradually increasing morsel size.
4. Regarding the anemonefish: they will find it ---do NOT rush them. I once had an A. frenatus
take five freakin' weeks to move into an E. quadricolor
like yours. Count your blessings ---once the anemonefish move in, it will be harder to revive any ailing anemone, if only for their sheer pestering.
5. To deal with pesky shrimp/fish make a 'Betsy' feeding tube out of clean plastic gutter screening:
Roll a piece of that plastic screening to a tube that's bit more than the diameter of your anemone, long as the water depth in your tank, and thread some nylon cord to stitch it together. Every feeding, position the tube upright and over the anemone avoiding contact with it! You will have thus fenced it in, and then you feed it, the tube protecting against thieving shrimp or fish.
This trick is a very old one ---the reason some of us call it a "Betsy" tube, is to recall the hobbyist (a Spanish-Australian-Filipina hottie too, haha) back in the 70's who taught LFS owners here how to solve JUST the problem you're describing.
Of course, you take the tube out once the morsel has been securely ingested at every feeding. Over time, the anemone will get faster and faster at claiming its meal, and you may no longer need the tube.
PS: My wife is also named Betsy, but I met her over a decade later
...and she actually puts old grey-eyes to shame, haha