Would I Be Entitled To Money Back After Falsely Being Accused Of Stealing From The Register?

I work at a Wendys restaurant and was being trained on the window register. I was doing fine for about a month, but one day my manager called me in and told me my register was short by an X$ amount? It was roughly $200.

After a day of him going through the system (no idea if he checked cameras), he told me I needed to put up the money. I begrudgingly paid, although I knew for certain I did not take any money.

2 weeks later I found out there was an issue in how I processed cash payments? So the correct amount was collected, but not recorded properly. This probably could have been corroborated by going thru each transaction, which i assume would’ve been tedious.

Anyways, mgr refused to pay me back the cash and told me he gave me extra hours to compensate. I was pissed, but i really need this job to pay for college. Should I have continued to ask for this money back/esclated?