Practitioners of mindfulness soon realize compassion is a key component of mindfulness. There is self-compassion and compassion for others. If you can’t be compassionate with yourself how can you be compassionate to others?
In fact there are even specialized meditations that focus on compassion.
I would argue if you can’t exercise compassion for yourself you may be setting yourself up for undue misery. Assume a terrible event has occurred in your life and you are bothered with it. You can be bitter and resentful if you react to that terrible event leading to emotional upset. Or you can respond to that event by showing some compassion to yourself. Through showing this compassion you may overcome the event, learn to accept it and believe it or not you might even be thankful for the event or it may be a combination of all three. You can’t truly escape sorrow but you can “manage” it so it does not become self destructive.
I refer to the “arrow story” for a bit of analogy. You are shot with an arrow and are in pain. If you start criticizing yourself for a myriad of reasons for being an easy target you are heaping fuel to the fire accomplishing little but adding to your pain.
Assuming one is not a psychopath or sociopath compassion is infinite or can be infinite.
It is as simple as closing your eyes and giving yourself or anyone else compassion. Recognize the sadness, anger or whatever the negative emotion is swirling in your head and send kind wishes of health, safety, understanding and in some cases forgiveness. Compassion has become so important there is actually a companion to mindfulness called compassionate cultivation training. Compassion does lead to a degree of neuroplasticity.
Empathy can be somewhat tricky in mindfulness. Empathy is in essence connecting with yourself or a third party and can be painful and draining. Perhaps instead of feeling for yourself or that third party send out thoughts of compassion.
Listen to the following short talk by author Paul Bloom on compassion vs. empathy. https://mindfulnessexercises.com/empathy-compassion/