憾

Left heart radical, the upright side form of 心. Indexes 憾 in the emotion-and-mood family (情 feeling, 怀 to harbour, 悔 to regret). Regret is felt rather than thought, so the heart on the side gives the picture: emotion sitting in the chest, hand-on-heart sense of loss.

Right 感 supplies the sound gǎn → hàn through a regular k/h alternation and pulls a clear semantic load too — 感 itself already means 'to feel.' Adding another heart on the left intensifies it: 遗憾 deep regret is feeling-on-feeling, a sentiment heavy enough to deserve doubled emphasis.