I overdrafted my account trying to buy a part for my car, but never actually *bought* anything. How do I get it back?

So last Sunday, I needed to buy a distributor for my car. A local Autozone had one in stock, and I went to go pick it up. I knew it'd be close to zeroing out my account as I was a few days away from payday, which, at the time, wasn't an issue and I needed the part. The total came out to around $260 after applying a discount. I used my chip enabled debit card, and the balance left after hitting zero in my account was about $60. So I returned some other items I'd bought the day prior at another AZ and had enough cash in my pocket to cover, but the register didn't like me trying to use three different payment methods. We tried it again, and my card was automatically declined. The clerk had told me it shouldn't have charged my card since there was no receipt printed out on their end. Well, incorrect, as there is a posted charge for $193 on my account and I have nothing to show for it.

Is this a case where I request a chargeback from my bank or should I go to that same store and see if they can refund me that in cash? I've never had this happen before and the only proof I have of the transaction is the cleared charge on my account statement and maybe something on my account in their system. I'm not hurting for the money, but I'm also not giving a company nearly $200 for nothing.