The actor plays Texas Ranger La Boeuf in the Western movie - written and directed by Ethan and Joel Coen. The character needed large sideburns and a moustache, but Damon explained that he found it difficult to grow them to the desired length.
The Belfast Telegraph quotes him as saying: "Luckily they can glue those on because I can't grow them that big."
He added that wife Luciana Barroso was not best pleased with the fake facial hair, saying: "I wish I could [grow sideburns] but then I'm not sure my wife would be too happy with them. They had a lot of people on hand to help make me look good in this movie."