As a further development of counting parts, it is worth practicing singing what you play, concentrating on one part at a time at first. To do this, you make an imitation of the sound of a particular drum or cymbal with your voice. E.g. for the bass drum you could sing "bom", for the snare drum you could use "dut" and for the hi-hats you could use "tsst".
These are only suggested sounds, so if you feel comfortable with others, use them instead. Singing a particular part helps focus your attention on that part and whether you are playing it well or not. Try playing through a drumbeat three times in a row, first singing the hi-hat part, then the snare drum part, then the bass drum part. As you focus on each part, be careful that your other parts don’t become unsteady. To help things even further, it is useful to program your beats into a drum machine and sing each part as you play along with it. If you do this regularly, your time feel will improve dramatically.