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.
Warmbier's release came amid mounting tensions with Washington following a series of missile tests by Pyongyang, focusing attention on an arms buildup that Pentagon chief Jim Mattis has dubbed "a clear and present danger to all."
His father, Fred, lashed out at North Korea last week, telling a news conference, "there is no excuse for any civilised nation to have kept his condition secret and denied him top-notch medical care for so long."
In their statement Monday, Otto's family said they believed the young man had found a peace of sorts after being flown home.
"When Otto returned to Cincinnati late on June 13th he was unable to speak, unable to see and unable to react to verbal commands. He looked very uncomfortable -- almost anguished," they said.
"Although we would never hear his voice again, within a day the countenance of his face changed -- he was at peace. He was home and we believe he could sense that," they added.
"We thank everyone around the world who has kept him and our family in their thoughts and prayers. We are at peace and at home too."
Three more US citizens are currently being held by North Korea, including two men who taught at a Pyongyang university funded by overseas Christian groups, and a Korean-American pastor who was accused of espionage for the South.