The actor rose to international fame playing Nicholas Brody in hugely popular TV drama Homeland.
He also has a busy family life, raising two children - Manon, seven, and six-year-old Gulliver - with his actress wife Helen McCrory.
"There is a lot of guilt that comes with this job because you often go away for three or four weeks at a time," he admitted to the latest edition of British InStyle magazine.
"The only reason Homeland works for our family is because two of those months are the summer holidays. And because Helen's self-employed, she can choose to be off and bring the children to be with me for two months. If she had another job I probably wouldn't have done the show because I couldn't have been away from them for that long."
Damian, 42, also indulges his love of fashion for the magazine by partaking in a stylish photoshoot.
The redheaded actor looks suave in a pair of Salvatore Ferragamo sunglasses, a Burberry Prorsum coat and a Gucci sweater.
He takes great pride in his sense of style and believes there are many things a man should know how to do, such as put on a tie.
"I stubbornly refuse to let my wife fasten my cufflinks because I think a gentleman should know how to do it himself," he also added.
"But when you get to the left hand it's hard. My tip is to buy a swivel-head type rather than chain-style cufflinks because they're easier to work with."
Damian also teased fans about what they can expect from upcoming seasons of Homeland, describing his character's journey as "complex and riveting".