Originally Posted by Retro Grouch

I'd take the wheel apart and get the right length spokes. While there's a possibility that you might get it to work, since you're talking about "several millimeters" almost surely the nipples are going to run out of threads and bottom out and you won't be able to get the wheel tensioned and trued.

As a general rule when you discover a screw up, the sooner you turn around the better.