Mr Trump made the comments following the death of 22-year-old Otto Warmbier, who was returned to the United States on June 13 in a coma.
"A lot of bad things happened but at least we got him home to be with his parents, where they were so happy to see him even though he was in very tough condition. But, he just passed away a little while ago," he said.
"It's a brutal regime and we'll be able to handle it," he added.
Earlier, Otto Warmbier's family released a statement confirming his death.
"Unfortunately, the awful torturous mistreatment our son received at the hands of the North Koreans ensured that no other outcome was possible," his family said.
Warmbier was imprisoned in North Korea for 17 months before being returned home in a coma less than a week ago.
Cincinnati doctors said he had suffered an extensive loss of brain tissue and was in a state of "unresponsive wakefulness", but it wasn't clear what caused his injuries.
Pyongyang said that Warmbier fell into a coma soon after he was sentenced in March last year for stealing a political poster from a North Korean hotel.
Warmbier's parents were told their son had been in a coma for more than a year, after contracting botulism and taking a sleeping pill.
He was sentenced in March 2016 to 15 years in prison with hard labour, convicted of subversion tearfully confessing to trying to steal the banner, calling it the "worst mistake" of his life.
