If you haven't cut the groove for the panel yet you can use a slotting cutter to do it to the size of the glass you choose. Slotting cutters come in many widths.
If the groove is already cut, only 2 choices I can see. One, put a bead of colored silicon in the groove to take up the slack. Two, cut the back of the groove off creating a rabbet and cut a moulding to hold the glass from the backside.
Someone I consider a master woodworker once told me that a master woodworker is not someone who never makes mistakes. He is someone who is able to cover them up so that no one can tell.