When I Couldn't Keep My Mouth Shut at Work

Last night, I was closing the bar when this guy starts complaining about his drink. It wasn’t my fault, but he wouldn’t shut up. So, I told him to get lost and not come back. He tried arguing with me, saying he paid for his drinks and has a right to stay here. Well, I’ve had enough of customers like that. Told him straight out: ‘This isn’t your home, this is my work. You can take your complaints elsewhere.’ He stormed off, and all the other customers cheered. Now everyone thinks I’m the bad cop at work. So, am I just being too harsh, or does he deserve it?