Can someone explain the emotional difference between 'Sadness' and 'Han'?

I’m practicing a deep vocal track for my next monthly evaluation evaluation tape. My Korean friend told me, "Your pitch is perfect, but you're singing it with Western pop sorrow. You need to sing it with 'Han' or 'Jeong'."

I Googled it, and the translations are so deep. It's like a mix of deep regret, collective sorrow, but also resilience? 🌊 As an international kid, how do I capture a cultural emotion that doesn't even exist in my native language? Are there any specific K-pop songs that are good for practicing this exact traditional emotional depth?