Last week's attack prompted Washington to launch a barrage of Tomahawk missiles on a Syrian air base.
Mr Trump's comments came as his administration slammed Russia's support for Syrian leader Bashar al-Assad, and questioned the Kremlin's interference with elections in Montenegro.
Rex Tillerson and Sergei Lavrov met in Moscow on Wednesday.
The United States and Russian Federation on Wednesday both presented souring views of the relationship between their two countries, exchanging sharp words as Moscow extended an icy welcome to the United States' top diplomat in a face-off over Syria. "There is a low level of trust between our two countries". We don't know whether those dead children were killed in Khan Sheikhun.
Putin said Wednesday that U.S. -Russia relations have "degraded" since President Trump took office.
Both Lavrov and Tillerson made mention of plans to establish a working group with representatives from the State Department and Russia's foreign ministry with the goal of improving relations between the two nations.
Dmitry Peskov on Thursday said that the tone of the meeting had been "fairly constructive".More news: World's oldest person Emma Morano dies in Italy aged 117
More news: Promotion is the only priority for Newcastle, says boss Rafa Benitez
More news: Thousands of evacuated Syrians stuck as transfer stalls
The United States responded to the gas attack by firing 59 cruise missiles at a Syrian air base.
The palpable tension hanging over Tillerson's trip spoke to a widening chasm between the former Cold War foes.
Sergey ZLavrov Russian foreign minister: We have said that there needs to be a very thorough investigation into this incident.
In a White House press conference with North Atlantic Treaty Organisation secretary-general Jens Stoltenberg, Mr Trump defended the decision to bomb a Syrian airfield after a chemical attack on civilians, stating Russian Federation "could have known" about the attack and chose not to stop it.
Lavrov is also subtly mocking Tillerson for the fact that top U.S. State Department positions are unfilled.
"Let us view this moment of crisis - and it is a moment of crisis - as a watershed and an opportunity for a new level of seriousness in the search for a political solution", said De Mistura. "Putin is backing a person that's truly an evil person".
"I think aligning yourself with Assad is a big mistake because he's a butcher, and I think it's very bad for Russian Federation", he added. "I think it's very bad for mankind", Trump said.
At their bilateral press conference, Tillerson left open the possibility that the USA might move to charge Assad with war crimes, although he said sufficient evidence to formally level such an accusation had not yet been amassed.