Learn English – Word for going through the motions / doing something because you are supposed to

I use perfunctorily a lot.

Then I learned I use it wrong.

I thought it meant to do something dispassionately or because you have to or to go through the motions. But actually it means

carried out with a minimum of effort or reflection. (NOAD)

Now, this isn't too different from the meaning I thought, because if you are doing something dispassionately or by obligation or are just going through the motions then you will carry it out with minimum effort or reflection, but the definition does not capture all that I thought it did.

What is the word that I want?

I fear I am not being clear. I fear that my desired definition and the real definition are too similar.

My desired definition includes "carried out with a minimum of effort or reflection" but it also includes a sense of obligation. You can do something with minimal effort because you want to do it but are just low in energy or because you are distracted or because you are hurried. The word I seek would make clear that the minimal effort is due to a lack of care—perhaps even more than a lack of care: maybe even disdain for the task.

This word would probably perfectly describe how most of us would perform tasks at a minimum wage job we have held too long. We would do it, maybe even well, but without any real care for it.

Another example. I ask this question now because I was going to write that people often pray "perfunctorily"—it is not heartfelt; it is done because people think that prayer is supposed good and important, but don't actually feel that it is.

I tried to find the word I want.

• Cursorily, briefly, hastily include an aspect of speed. The word I seek doesn't need to mean the action happened quickly; indeed the lack of desire might even mean it happens slowly.
• Dispassionately does not incorporate the sense of obligation.
• Obligatorily does not incorporate the lack of thoughtfulness. You can do something obligatorily and meticulously.
• Going through the motions is probably closest but, being a phrase, is difficult to turn into an adverb or even adjective. (Alternate, lesser answer would give me going through the motions in adverb form.)