I always see regret with an s
I have no regrets
isn't regret uncountable. It's a feeling.
It's possible to say " I have no regret" too.
and the noun after "no" should that always be singular or plural?
In addition, both have no regrets and have no regret are possible. The former refers to more than one regret, whereas the latter refers to a specific regret:
1. Robert Brault quote - Today I bent the truth to be kind, and I have no regret, for I am far surer of what is kind than I am of what is true.In short, the noun regret is countable; e.g., I have one regret; I have many regrets.
2. I have no regret leaving law for shoe making.
3. Normally I would not reveal so much about a film in case readers may be planning to see it, but in this case I have no regret in doing so.
Does that help?