The Unintended Consequence of Efficiency

So here's my story. I work night shifts at a busy 24-hour convenience store. One night, we were swamped with customers because it was just after the local bar had closed and everyone was coming in for snacks and drinks. I've always been proud of how efficiently I can handle these rushes without letting anything slip by me. That night, however, my efficiency backfired horribly on me. A woman came in looking pretty disheveled, clearly drunk. She wanted to buy a large soda bottle but didn't have enough cash on her, only about half the amount needed. Now, one of our policies is that we don't accept IOUs or partial payments. But this customer was desperate and kept asking me if there could be an exception just this once. Feeling bad for her and trying to stay efficient, I suggested she get a smaller size instead. She argued back angrily about how unfair it was to treat her like that. So, in my haste to move things along, I lied and told her we were completely out of the soda altogether. This way, it seemed fairer than rejecting her half-payment. She stormed off muttering under her breath about the 'unhelpful staff.' Later on, she came back with a friend who was even more irritated. They complained loudly to my manager. Now, I'm not usually one to let mistakes bother me much, but this has been gnawing at me ever since. Am I truly the asshole here for lying about being out of stock? Or is it the policy that needs adjusting to handle these kinds of situations better?