It probably wont be a problem (hard to tell without seeing it), but you are really concerned, you can take a popsicle stick or two and fill the gap some if it will squeeze in.
The other thing you can do is, like you tried, use cardboard, cloth, or styrofoam, depending on the severity. The tanks nowadays are pretty strong anyway, I wouldn't worry about it so much. Try the popsicle stick trick though if you think it might add some support.