The Prime Minister insisted that military action against Bashar Assad’s regime was a limited strike in response to the “harrowing” chemical weapons attack in Douma and was not about regime change.
But Mrs May also drew a link with the nerve agent attack on Russian former spy Sergei Skripal and his daughter Yulia in Salisbury.
Looking drawn as she spoke to reporters in Downing Street in a hastily arranged press conference, she said: “We cannot allow the use of chemical weapons to become normalised - either within Syria, on the streets of the UK or elsewhere.”
President Vladimir Putin has said Russia will call an emergency session of the UN Security Council over air strikes on Syria.
Asked if the strikes had also been a warning to Russia, the PM said: “The action that took place last night was an action which was focused on degrading and deterring the operational capability and the willingness of the Syrian regime to continue to use chemical weapons.
“There have been many instances when we have seen them using those chemical weapons.
“But I believe it should also be a message to others that the international community is not going to stand by and allow chemical weapons to be used with impunity.”
Mrs May said chemical weapons had “all too often” been used in recent times.
“I think it is right that the international community has come together and said we will not accept this,” she added.
The UK, United States and France launched “precision strikes” in Syria overnight.
US President Donald Trump announced the “combined operation” on Friday night and Mrs May spoke soon afterwards to explain her decision.
Labour leader Jeremy Corbyn said the military action against Syria was “legally questionable” and makes real accountability for war crimes less likely.
Mrs May has faced criticism from across the political spectrum for failing to recall Parliament and put the plans to a vote.
The Prime Minister said she will go before the Commons on Monday to answer questions about her decision but insisted there was no “alternative path”.
Mr Trump said the Syrian regime’s use of chemical weapons on Douma was a “significant escalation in a pattern of chemical weapons use by that very terrible regime”.
Following the announcement, the US said strikes had been launched at 9pm EST (2am BST) and had destroyed important infrastructure at three sites connected with the Syrian regime’s chemical weapons programme.
General Joseph Dunford, chairman of the US Joint Chiefs of Staff, said the first was at a scientific research centre in greater Damascus, involved in the development and production of chemical warfare.
Other strikes targeted an army depot near Homs.