Does the cat know that he made a mistake?
cats have no sense of right and wrong. They can't understand why knocking over a glass of water, turning the trash out of the trash can, or scratching the furniture can cause inconvenience or bad things to us. However, they do measure our reaction to things and they will remember whether they did something that upsets us or gets angry.

Then they will store this information in long-term memory. Cats react to our tone, the facial expressions we pull, and our body movements. Over time, they gain experience with the different things they do, and whether they are good or bad depends on human reactions.
cats see themselves as part of our family, which is part of their way of building a safe relationship. If we play and hug with our cats, they will feel safe. If we get angry, yell or curse, they will feel threatened and scared.

They want to feel safe again in their own social group, so they may do something to please others. This seems to be an apology to us because we often anthropomorphize cats. This means that we attribute human behavior and characteristics to them, believing that they have the same meaning, but in fact they do not.
So next time they kick the garbage on the carpet, don't care too much, they do this not out of resentment. They act just by impulse and instinct .
How do cats make up for their mistakes?
If your cat does something that upsets you and you react, they usually run away and hide. You may find them peeking at you.
Many owners often think it is their cat staring at them provocatively and silently say, "Yes, it's me, what are you going to do?" It's understandable that they think so, because it seems that they do it. In fact, they stare at you and want to guess your mood, because they will only relax when you are relaxing.

When you calm down, your cat will try to correct this situation. They slowly approach you. This action means they feel safe and they want you to be the same.
They may also start to hit you with their heads or rub your body against you. This is a way they deliver odor to us. This is usually a territorial odor marking behavior—your cat rubs against you with their odor glands, and you are "marked" by their odor.
This helps them recognize that you are a safe person they can trust. They may bring their favorite toys for you to play with. The cats will also whine around us, letting us know that they want to connect with us again. They may also knead on our knees with their paws. These are signs of their satisfaction. Another thing the cat does is blink slowly during eye contact. This is considered a way for cats to let their owners know they feel safe. Blinking slowly is a gesture of acceptance, and they do so to show their trust.
Summary: cats will not apologize to their owners. They change their behavior after doing something that causes negative reactions to humans. Cats don’t feel guilty, however, we do think cats feel connected to us and see us as part of their social group. Cats like to feel safe and secure in their home environment. Any threat to them is a destruction of their peace.
If your cats show love for you after doing something naughty, they do this because they don't like your reaction and they want to change it. They don't show self-blame, what they do is try to restore good relationships with cat parents so their social groups will be harmonious.