It may not be allowed depending where you live. Some states prohibit a business deducting shortages from employees' pay. I was surprised to read this, but apparently, it's not illegal. It becomes illegal if as a result, you are earning less than minimum wage.
Modern terminals tell the operator how much change to return to the customer. If you can't learn to count money, find another job. How did you get to be old enough to hold a job without being able to count change? How do you know you're not being ripped off when YOU buy something and get change back? You pay attention then, right? You have to on the other side of the register, as well. Letting you pay back the till makes it look like 1) you're getting a loan from the store or 2) management is taking advantage of you. It's in their best interests if you can't handle this task correctly, to hire someone who can, not take money out of your pocket every shift. No matter how much you like this job, there are tons of people who CAN make change correctly.
The only other thing to consider is whether someone else is using your till, as Jay mentioned. He's not the only one who's experienced that. My neighbor worked in a family owned store and the owner's son was pilfering money from the till.
You can continue to ask the question, but it's not complicated, people understand it, and they're giving you the answer.