To be sure of a sound attachment, you need to attach into the concrete. Anything else will almost surely fail. Plaster does not have the structural strength except where you can spread the load over a large area from behind the plaster, and even then it is iffy.
As suggested by others, to attach to the concrete, you can use tapcons, concrete expansion bolts, or expansion anchors that you put screws into. Any of these will make very small holes in the concrete and not compromise its strength. These holes could easily be filled when you leave.
SUPPLEMENT BASED ON COMMENTS:
You need to know what you are drilling into if you go that route.
A very different approach would be to create what is basically a free standing rack and then fixing it lightly to the wall.
The existing rack could be screwed or bolted to the top of the face of 2 upright hardwood boards, maybe 1x3s, as tall as you need the rack to be. The bottom of those uprights would be attached to a foot extending out from the wall about 12 to 15 inches. A brace would be attached on a 45 degree angle from the far end of the foot to a spot on the upright about 12 inches up.
The braced feet will counteract the downward pull of the coats. You could even attach a flat board to the tops of the feet to make a shelf for shoes, etc.
This whole unit could then be screwed into the wall through the uprights into plastic anchors in the drywall. This is just meant to keep it from shifting, not supporting the weight of the coats.
Since you already have a wall paper finish on the wall and you are hesitant to move the towel bar to another location this does put a damper on the types of solutions that could be used to fix this problem. By the way; Don't feel too bad about the failure. It is very common to find towel bars attached just into the drywall. :-(
The normal "robust" way to fix this would be to make a hole in the drywall near where the mount ripped out of the wall. Such hole would be about 2" (5omm) high by 4" (100mm) wide. A piece of wood with string around its middle would be placed down into the slot and then raised back up inside the wall using the string to pull it back up so that it was centered over the opening. A 3.5" (85mm) wide by 8-12" (200-300mm) long board would be used for this. Holding the board in place with the string, you would install drywall screws through the exiting wall board and into the wood to hold it in place. Patch up would consist of cutting a small piece of new drywall to fill in the slot hole and screwing it in place. Drywall taping, mud and sanding would be done to finish the wall back to a nice finish so that it could be re-painted. With this scheme the towel bar support can now be re-installed using longer screws to reach into the wood support that was added. The wood support spreads the stress of the towel bar across a much greater area of the wall preventing future tear out.
Now that you have a picture of what could be done let me suggest an alternate approach that will provide a strong support and permanent fix. For this you would remove both towel bar brackets and install a primed and pre-painted horizontal board across the wall in line where the towel bar mounted. You would secure this in place using screws into the nearby studs. If the towel bar was mounted in a narrower wall segment it is best, from a looks standpoint, to extend the board across the width of the wall. After the board is mounted in place the screw holes would be filled with spackle, sanded and touch up painted. The towel bar is then mounted onto this painted board.
With this latter approach it may be desirable to size up the room and if there are other towel bars present you may want to install these board strips in a uniform manner for those as well to maintain a style in the room.
If you saved some of the original wall paper it is also possible to glue wall paper onto these strips after they have been primed. Done carefully the wall paper pattern can be matched to the wall and make the towel bar mounting boards hardly noticeable.
Best Answer
I would use a jab saw to enlarge the hole. Then use a rod of wood and place it behind the spot your towel rack will eventually sit. (Make sure the piece of wood is longer than the towel rack bracket). Screw through the drywall above where the towel rack bracket will sit and below it. This will anchor the wood to the back of the wall while you patch the hole. Once that is done you can patch the hole with a pathig kit (ex. https://www.amazon.com/Wall-Doctor-Drywall-Patch-2)
Once you have let that set and cure you can remount your towel rack bracket. U can remove the extra screws and patch those holes over with a little spackling.