Initially, like the first oh 7-10 times of having anal sex, there will be a range of 'discomfort' ranging from burning sensation (from having friction in a place not designed to accept friction) to soreness, to even bogginess and down right agony.
The asshole is not designed to accept things being shoved up in it. It is an exit door only, it is actually designed to keep things out, thus you can can go swimming without getting your arse full of water. So there are what is called 'sphincter muscles' at the openig which are designed to allow fecal matter to pass outward, while preventing other things from easily going in.
If the burning sensation is around the opening of the arse, then its the sphincter muscles complaining, possibly even bruised or torn.
If the burning sensation is deeper, you could have scratched the anus/rectum walls. The anus/rectum and colon are composed of very delicate tissues which do not take kindly to any sort of friction. Again, the whole passage is designed to pass things down the line, they are not designed to take an object being forced in and out of it - no matter how slow and gentle you go it is forcing, since fecal matter tends to be pushed out with little resistance.
Thus its possible you have scratches, most likely microscopic. Being a moist area, any tears, scratches or other such injuries are less likely to scab over effectively, thus any opening in the tissue will be an open wound for longer than your exterior skin. Thus like a paper cut you feel a burning pain.
Lastly is the product(s) you use for lube and or the toys you use.
Dildoes are typically made from latex now days. If you are sensitive to latex or down right allergic, then a burning sensation will persist as you will have an inner ass rash. A good way to test an allergy to latex is to get latex glove, cut off the bottom one inch or so wrist part of the glove and wear it for a couple hours around your wrist.
If at any time during that period you start to see redness or feel itching take it off and you can pretty much say you are allergic to latex. If after two hours nothing happens, take it off and wait 24 hours. If redness or slight itching starts during that period and you haven't been exposed to anything like poison oak/ivy chances are high that you are latex sensitive.
If you are latex sensitive there are vinyl and sheepskin condoms you can use.
https://www.google.com/?gws_rd=ssl#q=vinyl+condoms has other types of plastics (non natural latex) condoms. Mind Sheepskin is literally sheep, and is not effective for stopping STDS, but is effective in protecting you from your Latex Dildo of Doom.
The other aspect here is your lube. Some people are sensitive to down right allergic to the lube. The best way to check that is to take a dime sized dot and put it on the inside (bottom side) of your forarm, about hand width up the arm from the wrist. Leave the dime size dot there for ten minutes, then use a dry cloth to wipe off the excess, wait about two hours to see what happens.
Again, redness/rash/burning sensation means your allergic. After two hours wash off with soap and water and monitor the spot for the day and see what happens. If you react later than that you have a sensitivity.
Yes I'm saying wait a day with these tests. The tissues of the inner anus/rectum are far more sensitive and react more violently and rapidly to exposure to allergens/sensitivity products than the skin of your arm. The skin is designed to keep stuff out of the body, the rectum/anus and colon are all pretty much designed to absorb stuff like nutrients, thus you can take a suppository (pills you shove up your butt) and absorb the active ingredients.
Also, since you are using a dildo you can be pretty certain you are doing damage to the lining of your anus/rectum area. Micro scratches due to friction and unavoidable. Unlike your outer skin there is no outer layer of dead cells to protect the more sensitive tissue. So minor friction, no matter how much lube you use, will ultimately lead to minor, microscopic scratches which allow such things like latex and lube to get into your sensitive tissues.