A lot of Warriors fanfictions use human emotions to display what the characters are feeling. This is not necessarily a bad thing, but might take away from the story for some readers (I can't count the number of times someone's told me that cats can't smile). Here, I've outlined some basic cat movements and the emotions or human movements they can portray that will help you avoid these exact comments.
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General Body
tensing
When a cat tenses its body, this is usually a sign that it is under some sort of stress. The muscles tense up beneath the fur, usually combined with the fur bristling or standing straight up, and show either fear, anger or discomfort.
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relaxing
A cat relaxing its body is the opposite of tension. Fur returns to normal, hackles are no longer raised, and stress is gone.

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Ears
flicking
In Warriors, a cat might flick their ear to acknowledge that they heard their Clanmate's comment but choose not to reply. Some cats might also flick an ear in annoyance or to point another in a direction.
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pushed back
Ears pushed back are never a good sign. Usually accompanied by fur standing on end, tension of the body or bared teeth, this movement means the cat is either angry or scared.
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perked
This movement shows alertness or interest. Apprentices might perk their ears if their mentor is teaching them something they are passionate about. Cats will also perk their ears when hunting to help them hear more of their surroundings.

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Eyes
glimmers & glints
This is a very broad category. A glimmer generally has a more positive connotation than a glint and would be more likely to describe amusement, mischief or pride. A glint, with a slightly more negative connotation, would apply better to more negative emotions, such as anger, fear or hurt.
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flashes
Similar to glints, a flash is a fleeting moment of emotion in the cat's eyes. For example, a flash of fear might pass over their face, giving their eyes a brief, shiny look.
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cloudy vs. clear
This is a good way to show if a cat is lost in thought or alert. Clarity of the eyes shows that the character is present, while cloudiness does the opposite.
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widening
A cat might widen its eyes in wonder or confusion. Sometimes, it will also turn its head sideways.
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narrowing
Opposite of widening, narrowed eyes mean fear, anger or (in the more human, but not completely, sense) suspicion.

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Fur
'feeling hot'
A good way to show that the cat is embarrassed or, sometimes, crushing on another character. Since cats cannot blush, this is a great substitute for the action.
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bristling
When a cat's fur bristles or stands on end, it is either angry or scared. Usually accompanied by tensing of the body, bared teeth and hissing.
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fluffing
A cat fluffs itself up to appear bigger. This can be for a variety of reasons: fear, pride or indignation, to name a few.

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Nose
twitching
A twitching nose signifies that the cat has picked up on a scent. It might also twitch its nose in amusement.

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Paws
shuffling
Shuffling paws generally mean embarrassment or inability to answer a question. Might be accompanied with feeling hot under the fur (aka blushing).
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sheathing/unsheathing claws
A sign of discomfort or anger. Most likely to happen when the cat feels threatened or is preparing to strike.

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Tail
lashing
A lashing tail signifies anger or indignation.
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flicking
A cat might flick its tail in acknowledgement or dismissal. Flicking tails over a part of another characters body is also commonly used, and can be used as a teasing motion or something to similar as a human poke.
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bristling or fluffing
A bristled or fluffed tail, like the fur on the rest of the body, signifies fear or anger.
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drooping
Drooping tails can signify sadness or exhaustion. Generally tied to a negative emotion.
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twining
When two cats twine tails, it is a sign of affection.

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Teeth
bared
Usually used to signify anger or fear, and in accompaniment with tension of the body, bristling fur and unsheathed claws. A cat can also bare its teeth in a sort of 'grin' in Warriors, just to give it a bit more of a human motion.

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Tongue
sharing tongues
In Warriors, cats share tongues to show affection towards their significant other or towards another Clanmate. It is not expressly confined to couples, as the Clan itself is a family and share tongues frequently (even just to keep each other clean).
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licking chest
A cat licking its chest will do so either because it is cleaning itself or because it is embarrassed or being modest. In Warriors, cats often lick their chest when they are being complimented.

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Whiskers
twitching
Twitching whiskers have a lot of different uses in Warriors writing. They can be twitched in annoyance, amusement or anger (and a variety of other emotions that I will not list here).

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The basic moral of the story here is that cats cannot exhibit a lot of human actions that show emotion. While Warriors is a fantasy series and should be treated as such, sometimes it's nice to include some more cat-like movements in order to build up the characters more realistically as cats and not as humans.