Could a misdemeanor have an affect on my background check of me getting a job?

A year ago I got fined with possession of an open bottle of alcohol under the age of 21, understandable, whatever. But I go to the interviews, do great, say they'll have a look at my background and then never hear from them again. I then got a job offer from one job, and after going through the hiring process they called to ask me how I got fined with possession of alcohol, what I was doing and ect. I felt it was none of their business but I told them what they needed to hear in order to keep the job. I wasn't drinking, it was just in my car from one of my friends. Which didn't matter at the time. Could this be the main reason why I haven't been getting any job offers? I finally got a job after searching for over a year. I commend them, they took the time to hear my side of the story and I want this off my record.