Depends a TON on what's behind the panel.
The house I bought had two "out rooms" on the other side of the garage. Both had shelving installed and had been used by the previous homeowner for some level of storage. We wanted to combine the rooms, so we cleared everything out and removed the shelves. When I went to demo the wall, I found the entirety of both rooms subsisted of nothing but the wood veneer (maybe 1/8" thick). The shelves were screwed into studs. I wouldn't trust this to hold anything significant by itself, and it had only a few penny nails holding it on. Came off super-easy (great for renovations, not so much for anything else).
In my den, there's a different story. The wood veneer was put over drywall. The drywall itself will support whatever drywall will hold (probably a bit more with that veneer glued to it).
Your question here seems to imply that there's concrete some short distance behind the wall
I tried drilling into the concrete behind to fit the screws but seems like my drill can't make much of a dent.
Wrong tool for the job. You're almost certainly using a wood drill bit. What you want here would be a masonry drill bit. They make them for normal drills, but be sure not to use a hammer drill bit in a normal screw driver. I would buy something like a Tapcon here (or other masonry fastener) to fasten to the concrete.