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First of all, there is nothing inherently wrong with describing a character's psychological state and inner thoughts (thought I would suggest focussing on the emotional state rather than the psychological). This is something that only the novel can do, and therefore a vital element of stories that only a novel can tell. 

But that said, you should not do it as a lazy alternative to creating a drama by which we will perceive their emotions from the things they do and the the things that happen to them. This is to be preferred whenever it works. And this is not a matter of describing facial expressions or adding an adjective to the verbs that describe their actions. Saying, "Jeff frowned. 'Maureen has gone,' he said sadly." That is not showing through action. That is describing emotions really briefly. 

Human beings are naturally sympathetic and empathetic. When we see something happen to someone, we don't need to be told how they feel, because we feel it too. Just show us who the character is, then show us the event happening, and we will intuit the emotions for ourselves. Unless, of course, the protagonist's emotions are contrary to expectations. That is when it is useful to describe them. 

> Tim smiled inwardly as they threw the clods of earth onto his mother's coffin.

Tell us the thoughts and emotions that are contrary to expectations. Otherwise, let us figure them out for ourselves. 

And that is, ideally, how you want to end a chapter, by subverting expectations. Your current closing line is pretty mundane as it stands. But if the actions it describes are contrary to the reader's expectations, then those same words could be powerful. 

> The guard fastened the shackles to his mother's wrists and led her towards the execution room. He waved her goodbye, and then he sipped his cup of coffee while looking towards the window. When the elevator rang, he looked back at her with a smile to send her off.

Put it in that context and those mundane words suddenly become chilling. 

It is not about what the word are by themselves. It is about the effect they have in context. You don't need to subvert expectations at the end of every chapter. But you do want to do something to keep the reader reading, something to force them to immediately dive into the next chapter. 

Do I want to know what happens next to a character that sips his coffee and waves goodbye as his mother is dragged off to the execution chamber? Heck yes. 

As to your comment that the character you are describing is "extremely unimportant" to the story: in that case, they have no business at the end of a chapter. Beginnings and ends of chapters are the links that bind the story together. They are important. They need to concern important things and important people. Otherwise, why should the reader read on? 

If a chapter just seems to be petering out, then it is likely that the whole construction of the ending is wrong, and perhaps that the whole construction of the chapter is wrong. A chapter should involve at least one important change of value for an important character, and the ending should generally emphasise, or subvert, or hint at an upcoming reversal of that value. It should end with a bang, not a whimper.