"None of the combined aircraft or missiles involved in this mission were successfully engaged by Syrian air defenses and there is no indication Russian air defense systems were deployed", EUCOM said in a press release.
A local reporter for The Arab News said Israeli warplanes were spotted in Syrian airspace just before the missiles were reported.
Iranian news agencies also reported missiles being fired toward Shayrat.
He said: "Video shows Missile launched against unknown Target in Far East Damascus countryside".
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Syrian state media is widely believed to exaggerate their claims of shooting down incoming missiles.
The Pentagon said there were no reports of USA military activity, after reports from Syrian television that Syrian air defences responded to a missile attack over Homs which targeted Shayrat air base late Monday night. Reports close to the regime indicated that its defences shot down six missiles targeting the base. The attack, involving 59 Tomahawk Land Attack Missiles, came as a response to the alleged use of chemical weapons in the Idlib Governorate on April 4.
Pentagon spokesman Eric Pahond said there was "no United States military activity in that area at this time", according to The Jerusalem Post.
Syria denied it was responsible for the attack, which killed at least 80 people. Social media reports are pointing the finger at Israel for the strikes.