Oksana Grigorieva and her lawyers touted her music credentials in court this week, but we now know exactly how Mel Gibson feels about her music -- he says it sucks.

Sources connected to Mel tell TMZ ... Gibson deeply regrets supporting Oksana's music career -- especially plunking down a fortune to produce a CD and music video. Mel even paid for a studio in Oksana's home.

Mel privately says Oksana's voice and music are "horrible," and he's "embarrassed" that he promoted her.

So that's Mel's opinion. Listen to :30 seconds of an Oksana song, and then tell us ...