2 C clamps, a 2 foot long 2×4 or any scrap wood that you have would work, and some adhesive (like liquid nails)
You want to get as far back under the veneer as you can with your adhesive without pulling more up. Once you have the adhesive down, clamp down the wood with the C clamps. You could even just set a few books on top of the part you glued. Make sure to wipe any excess thay oozes out with a damp paper towel.
Let dry, and you should be good to go