The British musician, who does not have a driving licence, moved his dad's car in a parking lot in Leicester, England in May (14), but accidentally hit the accelerator pedal instead of the brake and knocked him down.
Meighan's father, also named Tom, was hospitalised to treat his injuries, and he has since made a full recovery, but the star admits he is still wracked with guilt.
He tells Britain's Daily Mirror newspaper, "It was a freak accident, it was horrible. That was the worst day of my life. I can drive but it was in an automatic car. It was too fast. It was a real shock at the time. It would only happen to me. We have laughed about it now and that's all you can do. I'm very close to my dad. He's a very amazing person to have around, so that happening was awful."
The accident happened just weeks before the band played a career-defining headline set at Britain's Glastonbury festival last month (Jun14).