"I find it very disappointing but sadly I have to tell you not all that surprising," Tillerson added.
Tillerson, in Florida to attend a summit between Trump and China's Xi Jinping, is due in Moscow next week for talks with President Vladimir Putin.
In Washington, a senior US official said Syria may have had help carrying out the alleged chemical attack, but stopped short of accusing Russia of complicity.
"We are carefully assessing any information that would implicate the Russians knew or assisted with this capability," he said.
The day also saw US Ambassador to UN Nikki Haley delivering a warning that the attack was only first in many more to come. She was speaking at an emergency session of the UN Security Council called after the US strikes, which were launched to punish an alleged chemical weapons attack by Bashar al-Assad's regime.
"The United States took a very measured step last night," Haley told the council. "We are prepared to do more, but we hope it will not be necessary."
Fired from the USS Porter and the USS Ross, the cruise missiles targeted radars, aircraft, air defense systems and other logistical components.
The Syrian Observatory said the US strike on the base killed eight Syrian military staff, including an army doctor. Syria's army had earlier said six people were killed in the strike, without specifying if they were military personnel or civilians.