"We say that this resembles very much the situation of 2003 and the war in Iraq", Putin said Tuesday during a press conference in Moscow.
The U.S. received broad support from Europe after the airstrikes.
"Russia's initiative in 2013 to dismantle Syria's chemical weapons has been exposed as a shambles".
Mr Tillerson said there was "a low level of trust" between both countries and such a relationship could not be allowed to continue between the world's foremost nuclear powers.
The G-7 has called for an independent global investigation into last week's chemical attack in Syria, and Johnson says depending on what it finds "those responsible for unleashing those chemical weapons" could face sanctions - including Russian officers.
Trump says Syrian President Bashar Assad is "an animal".
Earlier in the day, G7 foreign ministers rejected British Foreign Secretary Boris Johnson's calls to broaden sanctions against Russian Federation and Syria.
Russia's top diplomat accused the United States of carrying out an unlawful attack against Syrian President Bashar Assad's forces.
"It's time for (Russian President) Vladimir Putin to face the truth about the tyrant he is propping up", Johnson said, according to a foreign ministry spokeswoman.
US officials, including UN Ambassador Nikki Haley and Secretary of State Rex Tillerson, said Syria's benefactor, Russia, was either complicit in the attack, incompetent, or played for a fool by Syria. He said the United Nations should first investigate the attack.
"These are the same people that said Saddam Hussein had weapons of mass destruction", the Trump transition team said in a statement.
Putin said on Tuesday Russia would be urgently asking the global chemical weapons watchdog - the Organisation for the Prohibition of Chemical Weapons - to investigate the incident.
Following on from the Tillerson visit, Moscow has announced Lavrov will host three-way talks with his counterparts from Syria and Iran later this week. In a briefing on Tuesday, they said that while there is no USA intelligence consensus on whether Russian Federation had advance knowledge of the attack, it seems implausible that Moscow wouldn't have known, given the close military cooperation between the two countries. It's unclear whether Putin will grant Tillerson a meeting.
Turkey last week conducted autopsies on three victims of the gas attack who were brought from Syria.