The rash of comments Sunday came amid an already intense back-and-forth between the USA and Russian and as Syria continued to be rattled by more lethal explosions.
The CBS host pressed Tillerson on saying there's been no change in policy regarding Assad, wondering if he was stating that the Syrian president's fate should be determined by the Syrian people.
"The real failure here has been Russia's failure to live up to its commitments under the chemical weapons agreements that were entered into in 2013", Tillerson said during an interview on ABC's "This Week," calling the attack a product "in large measure a failure on Russia's part to achieve its commitment to the worldwide community".
The White House says President Donald Trump spoke with Saudi Arabia's king about Syria and he "reaffirmed strong Saudi support for the United States' military strike against the Sayrat airfield".
"I don't draw conclusions of complicity at all, but clearly they've been incompetent and perhaps they've just simply been out-maneuvered by the Syrians", Tillerson said of Russian Federation.
But in the aftermath of the attack, Trump ordered the strike targeting the Shayrat air base in central Syria's Homs province with 59 Tomahawk missiles.
At least 87 people were killed - including women and children - in the assault on the Syrian town of Khan Shaykhun last Tuesday.
North Korean ballistic missile launch condemned by UN Security Council
However Reuters subsequently reported that White House officials determined the missile was a liquid-fuel scud . President Donald Trump in Florida, where North Korea is expected to be a prime topic of discussions.
Hundreds more suffered symptoms that the World Health Organization said were in some cases consistent with exposure to chemicals that include nerve gas.
Sadr became the first Iraqi political leader to call on Assad to resign even as he condemned the USA for the missile strikes on a Syrian airfield on Friday (7 April).
Tillerson is heading to Lucca, Italy, for a two-day meeting of G7 foreign ministers that starts Monday, and he will continue from there to Moscow for meetings with Sergey Lavrov, his Russian counterpart, and other Russian officials. "The failure related to the recent strike and the recent awful chemical weapons attack in large measure is a failure on Russia's part to achieve its commitment to the worldwide community", he added.
"I'm disappointed in that response from the Russians because it indicates their continued support for the Assad regime", said Tillerson, who is expected to make a hard trip to Moscow next week.
The move immediately prompted a backlash from Russian President Vladimir Putin, who said it would damage U.S.