What kind if fabric is it? An open weave may need something fused to the back so the edge doesn't fray out. If that is the case I would fuse a piece of fabric to the underside first if you can get the iron in there. If not, put some fray check along the edge and then use upholstery thread and a needle to mend the tear. I have used upholstery thread to mend a tear in a leather couch on an arm seam and it worked quite well.