The President was speaking during a Rose Garden press conference after he earlier said that the attack, which killed 86 people, was a “terrible affront to humanity”.
Up to 30 children and 20 women are believed to be among those who died after Tuesday’s alleged attack on the town of Khan Sheikhoun.
In response to a question from the media about a White House statement that blamed the attack in part on former president Barack Obama, Mr Trump said: "I now have responsibility [to solve this], and I will have that responsibility and carry it very proudly.”
He added: “It is now my responsibility. It was a great opportunity missed.”
Mr Trump said the attack crossed "many, many lines" and cannot be tolerated.
He said: "That attack on children yesterday had a big impact on me. Big impact. My attitude towards Syria and Assad has changed very much."
Mr Trump refused to reveal what action the US might take in response, saying disclosing military action ahead of time was a mistake the Obama administration had repeatedly made.
"I'm not saying I'm doing anything one way or another, but I'm certainly not going to be telling you," he said.
Mr Trump said the attack was "so horrific" and noted that it had killed "innocent people, small children and even beautiful little babies".
"These heinous actions by the Assad regime cannot be tolerated," he said.
As president, Obama backed away from military strikes despite warning Assad that using chemical weapons — as happened in a Damascus suburb in 2013 — was a red line.
MPs in Britain also refused to back military intervention in the wake of the attack. Turkey today said it had findings which indicate that the latest incident involved chemical weapons.
Russia’s defence ministry said the deaths resulted from a rebel chemical weapons depot being hit by Syrian government air strikes.
The Syrian government “categorically rejected” it carried out the attack, instead blaming rebels and accusing them of making it up to frame the regime.
However, Syrian rebel commander Hasan Haj Ali said: “Everyone saw the plane while it was bombing with gas.