It is not possible to put recessed fixtures into a concrete ceiling, but there are a few creative ways you can approach it. One possible solution is to install box beams (hollow beams) that run from wall-to-wall or installed a coffered detail. You can then place the recessed fixtures in the beams. It also means that you can install hanging decorative fixtures as well.
Another more modern solution would be to suspend floating wood or medium density fiberboard (MDF) panels which would hang down 3.5 inches from the actual ceiling. You can then put recessed fixtures in these panels as well as run a perimeter LEDs light for an attractive ambient glow. And if I were you, I would get rid of the popcorn. All you have to do is water it down and scrape it off. There are videos you can watch; just type in "how do I remove the popcorn ceiling?" into your search engine. If it is asbestos then you have to have a specialized company do the work. But if it has glitter in it, I would keep it.