At least six people are reported to have been killed in the US missile strikes early on Friday.
Syria's ally Russia accused the US of encouraging "terrorists" with its unilateral actions.
"I'm disappointed in that response," said US Secretary of State Rex Tillerson.
"It indicates their continued support for the Assad regime and, in particular, their continued support for a regime that carries out these type of horrendous attacks on their own people.
"So I find it very disappointing, but, sadly, I have to tell you, not all that surprising," he added.
Moscow has promised to strengthen Syria's anti-aircraft defences.
It is also closing down a hotline with the US designed to avoid collisions between their air forces over Syria.
According to Idlib's opposition-run health authority, 89 people, including 33 children and 18 women, died in the suspected nerve agent attack in the rebel-held town of Khan Sheikhoun on Tuesday. Syria denies using nerve gas.
The US ambassador to the UN Nikki Haley told an emergency session of the UN Security Council that the US had acted to ensure Syrian President Bashar al-President Assad would never use chemical weapons again.
"We are prepared to do more but we hope that will not be necessary," she said. "It is in our vital national security interest to prevent the spread and use of chemical weapons."
She blamed Iran and Russia for standing by the Syrian government when it committed crimes. "Strengthening Assad will only lead to more murders," she said.
Russia's deputy ambassador to the UN, Vladimir Safronkov, described the US strikes as "illegitimate".
"When you take your own path, this leads to horrible tragedies in the region," he told the Americans.
US Treasury Secretary Steve Mnuchin said he was preparing further economic sanctions against Syria.
America's weapon of choice: Analysis by Jonathan Marcus, BBC defence & diplomatic correspondent
Cruise missiles fly low and have a relatively small radar cross-section so they are difficult to destroy with air defences. Russia may seek to improve Syria's surface-to-air missile system in the wake of this US attack but it would be very much a case of shutting the stable door after the horse has bolted.
Syria used to have a highly effective national air defence system based on Soviet-era radars and missiles but it has been significantly weakened in the wake of the civil war and the loss of territory by the regime. Look at the ease with which the Israelis carry out strikes against Hezbollah arms convoys and weapons stores in Syria.
Russia has some of its most modern surface-to-air missile systems at its air base in Syria and radars with a huge reach but, for whatever reason, they too have not deterred Israeli strikes.
Their presence makes air strikes by manned US aircraft unlikely and for Washington the Tomahawk cruise missile will remain the weapon of choice.
Two US Navy destroyers in the Mediterranean Sea fired 59 Tomahawk cruise missiles at Shayrat air base in western Homs province at about 04:40 Syrian time (01:40 GMT) on Friday.
They targeted aircraft, aircraft shelters, storage areas, ammunition supply bunkers and air defence systems at the Syrian government-controlled facility, according to the Pentagon.
It said the base was used to store chemical weapons and that "every precaution" had been taken to avoid casualties. The Russian military was informed beforehand, the Pentagon said.
Syrian state media said as many as nine civilians had been killed in the strike, four of them children. The BBC is unable to confirm this information.
The Syrian army said earlier there had been significant damage to the base.
However, the Syrian Observatory for Human Rights, a UK-based opposition news service, said on Friday evening the base was already back in operation and aircraft had taken off and "struck targets near Palmyra". The report could not be independently verified.
The US has led a coalition carrying out air strikes against jihadist groups in Syria since 2014 but this is the first time it has targeted government forces.