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"He should have been brought home that same day. The results would have been a lot different," Trump said.
The Trump administration secured Warmbier's release from North Korea last week on humanitarian grounds after nearly 18 months of imprisonment. He arrived in the US last Tuesday in a coma and died on Monday.
Trump called the situation a "disgrace" and is now facing calls for the US to respond to North Korea for its role in Warmbier's death.
But on Tuesday, answering a question during an Oval Office meeting with the Ukrainian president, Trump focused on lamenting the length of Warmbier's imprisonment and the delay in securing his release.
"He should have been brought home a long time ago," Trump said.
Warmbier was arrested and imprisoned in North Korea during President Barack Obama's time in office, though North Korea only informed the US of Warmbier's medical condition earlier this month. Trump's comment could be interpreted as an implicit knock of the Obama administration.
Ned Price, former National Security Council spokesman under Obama, responded to Trump saying the Obama administration "had no higher priority than securing the release of Americans detained overseas."
"North Korea's isolation posed unique challenges, but we worked through every avenue available to us -- including through the Swedish, our protecting power, as well as through our representatives in New York -- to secure the release of Mr. Warmbier," he said, adding that at least 10 Americans were freed from North Korea under Obama.
Three Americans remain imprisoned in North Korea. Tony Kim and Kim Hak Song were arrested in recent months on charges of committing "hostile acts." A third American, Kim Dong Chul was detained in 2015.
"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," Trump said Monday, reacting to Warmbier's death.
White House press secretary Sean Spicer on Tuesday offered few details about how the US plans to respond to the death of Warmbier, promising only that the US will "continue to apply economic and political pressure" to change North Korea's behavior.
"The President has spoken very clearly about how he and the first lady and our country feels about the loss of this American," Spicer said.
Spicer said the US is continuing to work with China to apply pressure on North Korea and said the US has seen "positive movement" with China.
The US will "continue to work with them and others to put the appropriate pressure on North Korea to change the behavior of this regime," Spicer said.
Asked whether Trump would still consider meeting with Kim Jong Un -- as he previously said he would be willing to do, given the right conditions -- Spicer said: "Clearly, we're moving further away, not closer, to those conditions being met."
CNN's Kevin Liptak contributed to this report.