It’s a bit more than that – it’s the absence of God, and the full knowledge that the damned soul will never be in the presence of God and never experience the Beatific Vision.
And the soul is in Hell, of course, and fully aware of that, so there’s no denying or refusing to believe that it’s all real, that God, and Heaven and Hell, do exist.
So, yes, the absence of God and an eternity of regret.