Russian President Vladimir Putin is likely furious after the U.S. fired cruise missiles at a Syrian air base in response to a chemical weapons attack, former U.S. Ambassador to Syria Theodore Kattouf told CNBC on Friday.

"But they have egg on their face," Kattouf, who served under the George W. Bush administration, said on "Squawk Box."

Kattouf said that Russia guaranteed in 2013 that Syria's chemical weapons arsenal would be removed or destroyed. Obviously, that did not happen "100 percent," Kattouf said.

After Thursday's U.S. missile strikes on a Syrian air base, Secretary of State Rex Tillerson said Russia had failed to carry out the 2013 agreement to secure Syrian chemical weapons. He said Moscow was either complicit or incompetent in its ability to uphold that deal.

Russia said the U.S. strikes against Bashar Assad's government violated international law. Kremlin spokesman Dmitry Peskov said Putin believed the U.S. attacks on Syria showed aggression against a sovereign state.

President Donald Trump ordered the attack by 59 Tomahawk missiles on a Syria military air base in response to Tuesday's deadly chemical weapons attack allegedly carried out by Assad's military on a rebel-held area.

Kattouf said the strikes against Assad's government sent "just the right message."

James Stavridis, a retired admiral who served as NATO's supreme allied commander, told CNBC on Friday that the attack showed the U.S. is not afraid to use force.

"Let's face it: Part of the audience here is not just Russia, Iran and Syria. Part of the audience is (Chinese) President Xi (Jinping)," Stavridis said on "Squawk Box."

As missiles hit a Syrian air base, Trump was meeting with the Chinese president in Florida.

"Perhaps it is no coincidence that the strikes get launched while President Xi is down in Mar-a-Lago. Pretty good signal that the United States intends to play hard with North Korea," Stavridis said.

—CNBC's Everett Rosenfeld contributed to this report.