The star portrays a twisted cop in the crime thriller, and Harrelson believes it would have had a good chance at landing nominations for the recent Golden Globes and the upcoming Oscars - if it wasn't for the damaged screening discs and strict Academy rules.
He tells the Los Angeles Times, "It's just frustrating. They send out the screeners and they're defective; 3,500 defective screeners. They couldn't just re-send, either. There's a policy with the Academy that, unless someone asks - like, specifically writes a letter to ask - it doesn't happen."
With so many films to screen, Harrelson can understand why no one chose to request a replacement disc, but admits, "it's a bit of a bummer".
However, the actor refuses to dwell on the issue - he just wants film fans to check Rampart out.
He adds to New York Magazine, "Not to say we would have been nominated anyway, but defective screeners are kind of a shot in the foot. I don't care about awards. I just think it's a great movie, and I want people to see it."
Harrelson previously earned Oscar nominations for his acting in 1996's The People vs. Larry Flynt and 2009's The Messenger.