The phrase has been ruined slightly. Self-compassion, in much of its current packaging, suggests a soft voice, a candle, a permission to lower the bar. Most people who'd benefit from it react against that version on instinct.
The actual research is more interesting. Self-compassion — as Kristin Neff and others operationalised it — has three measurable components: mindful awareness of what you're feeling, recognition that suffering is shared (the felt sense that you're not the only one), and treating yourself with the kind of warmth you'd offer a friend in the same spot. The third one is the unfamiliar one. Most adults are markedly less kind to themselves than to the people they love.
Neuroimaging suggests the self-directed warmth activates similar circuits to receiving warmth from a trusted other. It is not soft talk; it is a regulatory mechanism. Animals that lick themselves are calming their nervous systems. We have a version of that, and it runs on a particular kind of inner address.
What helps is being specific. Not "I'm doing my best", which is too general to land. More like: "this is hard, and the part of me that's struggling has a real reason to struggle, and the version of me that's still here doing it deserves not to be hated for it." That kind of sentence, delivered to yourself in your own internal voice, is what the research actually points at.
It is not the same as letting yourself off the hook. People with stronger self-compassion are more likely, not less, to take corrective action after mistakes — partly because the shame penalty is lower, so there's more available energy to look at what happened.
The kindest people in your life probably don't speak to themselves the way they speak to you. The work is closing that gap.