"We of course know that our work in Syria is not done", she said.
"Everything that has strained the relationship is on Russia's side", she said, adding that the USA hopes for improved relations with Moscow, but that "we're not going to put up with bad behavior to get it".
American officials said the strikes were retaliation for a suspected.
The action was in response to a recent deadly attack in the town of Douma.
Trump tweeted "Mission Accomplished" on Saturday after U.S., French and British warplanes and ships launched more than 100 missiles almost unopposed by Syrian air defenses.
Ambassador to the United Nations Nikki Haley said there will be additional Russian sanctions.
Haley says the fact that Assad was making the use of chemical weapons "more normal and that Russian Federation was covering this up, all that has got to stop".
In the coastal city of Latakia, a northern province, hundreds of civilians congregated in Sheikh Dahir Square to express that the aggression against Syria failed because of the steadiness of the Syrian army.
Syrian President Bashar al-Assad's regime was suspected of orchestrating a chlorine attack, which occurred on April 7. "We know that it is now up to Bashar al-Assad on whether he's going to use chemical weapons again".
The remark came in a parenthical phrase during an interview on Fox News Sunday, as Haley blamed Russian Federation for strains in its relationship with the United States.
Russian Federation also decried the USA -led operation as a failure, saying the majority of the rockets fired at Syria were intercepted by the Syrian government's air defense systems.
"It's illegal because he didn't come and ask permission", he said.
Trump also said the term should be utilized more, exclaiming "Use often!"
Russian agencies quoted the lawmakers as saying that Assad was in a "good mood", had praised the Soviet-era air defence systems Syria used to repel the Western attacks and had accepted an invitation to visit Russia at an unspecified time. In a US military action a year ago in response to a sarin gas attack, the Pentagon said missiles took out almost 20 percent of the Syrian air force. Let the other people take care of it now [.] We're going to have 100 percent of the caliphate, as they call it, sometimes referred to as land. The U.N. Security Council met to debate the strikes, but rejected a Russian resolution calling for condemnation of the "aggression" by the three Western allies.
The strikes suggest that Trump may have reset America's red line for military intervention in Syria over the use of chemical weapons. The operation targeted three Syrian chemical weapons facilities - one in the capital of Damascus and two others near Homs, near the border with northern Lebanon.