The reason it sounds like crap probably isn't the UST ... especially if it sounded OK with steel strings.
As mentioned, nylon strings don't have the tension to drive a guitar top designed for light gauge steel strings.
Plaus, if you didn't adjust the rod, the neck is almost certainly backbowed if the rod works at all. You've got about 60% (or less) of the string tension you had before. Unfortunately, unless you've got a double action rod, that's probably out of the range of the rod. Try loosening it anyway if the neck's too straight or backbowed.
And, like someone said, you'd probably need to raise the saddle unless the action was high before.