Nikki Haley said her country would not stand by when chemical weapons were used, as it was in its "vital interest" to stop their proliferation.
Syrian ally Russia accused the US of encouraging "terrorists" with its unilateral actions.
Moscow has promised to strengthen its ally 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.
At least six people are reported to have been killed in the US missile strikes early on Friday. US officials say the base was used to launch a chemical weapons attack that killed dozens of civilians on Tuesday.
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. Syria denies using nerve gas.
Ms Haley told an emergency session of the UN Security Council that America 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.
UK ambassador Matthew Rycroft said the strikes were a "proportionate response to unspeakable acts".
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 airfield in western Homs province at about 04:40 Syrian time (01:40 GMT).
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.
Unnamed US intelligence sources have told media they believe Russian personnel were at Shayrat when Sarin, a nerve agent, was loaded on to a Syrian jet but they have not established whether the Russians knew it was happening.
Retired civil servant Mateea Zefa, who lives near the base, went with his children to look at the base afterwards and found it "totally destroyed".
"We saw lots of bombs," he told the BBC by phone. "Loads of them. It was a tough night. My house was damaged, almost all the windows broke and some walls cracked."
Houses on one side of the base were also "totally destroyed", he added.
Some children and other people were injured by shards of breaking glass but no civilians were killed, she said.
The dead and seriously injured were all soldiers, she said, adding that they had been brought to her hospital.
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.
President Trump previously spoke out against US military involvement in Syria, instead calling for a greater focus on domestic interests.
US Secretary of State Rex Tillerson signalled a sudden shift in policy on Thursday, saying that Bashar al-Assad should have no role in a future Syria.
Russia says it has formally notified the Pentagon that as of 21:00 GMT on Friday their air force hotline for Syrian airspace will close down.
It also sent a frigate armed with cruise missiles, the Admiral Grigorovich, from the Black Sea to the Eastern Mediterranean on Friday, in what may be a routine move.
The US envoy to the UN has warned America may take further action after bombarding a Syrian air base suspected of using chemical weapons.