The Frasier star's father was killed after being shot when his son was in his early teenage years.
Following this, his sister was abducted and murdered in 1975 at the age of 18, and his two half-bothers died in a diving accident in 1980.
In 2012, the actor and his wife lost a son in utero.
In an interview with Radio Times, the 61-year-old said: "I had a very spiritual youth.
"Then I had the challenges of a couple of really big tragedies.
"There was a time when I abandoned the effort to find a reason to be alive."
When asked if he lost his faith, the Cheers actor said: "I probably lost it.
"But things happened that said to me, 'Get up, Bambi.' I guess that's my raison d'etre: 'Go on, get up Bambi.'"
The US actor has been sober since spending time in rehab several years ago, after battling substance abuse problems during his time on the sitcom Frasier.
He said: "If I hadn't had adversity, I wouldn't be where I am."