It really depends on what you mean by "other rhythm games". It is entirely possible that you are in fact hitting notes with the same accuracy but said other rhythm games have a bigger perfect timing window that osu!mania does. Here, getting a perfect is about 42ms average? I think that's the value (someone correct me if im wrong), albeit it changes with Overall Difficulty (OD) slightly.
Other than that, there are the usual things like train/focus on accuracy, set universal offset properly (setting notes later is positive direction, setting them earlier is negative direction), and make sure you are comfortable with the skin you are using (if you want to make any slight adjustments like changing the lane width or horizontally shifting your playfield, you can do that in the skin.ini folder).