Mr Johnson, at a G7 meeting of foreign minsters, called for targeted sanctions against Syria and Russian diplomats until president Bashar al-Assad is ousted, but the group has responded saying President Putin "must not be backed into a corner" as it continues to seek diplomatic solutions.
A communiqué issued by the G7 made no mention of sanctions but included a significant new agreement that Mr Assad cannot stay on as Syrian president.
But the UK Foreign Secretary has insisted that Russia could still be hit with tough sanctions over its support for Syria despite being unable to build an international coalition to take on the Mr Putin.
Boris Johnson believes sanction could still be placed on Russia over is alliance with Syria
US Secretary of State Rex Tillerson has also told Mr Putin he hoped for a joint G7 position against Mr Assad and expected support from Middle Eastern allies in the wake of the deplorable chemical gas attack that killed 87 people a week ago.
Any sanctions against Russia, which has backed Mr Assad's regime for years, and Syria, will not be implemented until a thorough investigation into the chemical weapons attack on the rebel held area of Khan Sheikhun has taken place.
A Government source told the Telegraph Mr Johnson’s failure to secure an agreement on sanctions against Russia had been a considered a "total let down" and that his cancelled visit to Moscow has left Britain with credibility with the Kremlin.
Boris Johnson spoke with other G7 foreign ministers at a meeting on Monday
The Prime Minister and the president agreed that a window of opportunity now exists in which to persuade Russia that its alliance with Assad is no longer in its strategic interest
Downing Street spokesman
The source said: "He is now persona non grata with Russia, they won't take him seriously. He has blown his bridges with them by cancelling [a visit] for the third time.
"We have no credibility with the Russians and no additional credibility on the World stage following the G7. This has been a very negative experience."
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But a spokesman for Mr Johnson criticised such a view was “completely short-sighted and wrong”.
Russian and Syrian could still face sanctions with the G7’s blessing if an independent investigation proves Assad was to blame for last week’s chemical attack and that Mr Putin knowingly carried on backing him.
Mr Johnson as called president Putin to cut ties with the Assad regime in Syria
Horrific images depict sickening chemical gas attack in Syria
Tue, April 4, 2017
At least 58 people, including nine children, were killed in an air raid that released "toxic gas" on the rebel-held Syrian town of Khan Sheikhoun
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A child receiving treatment at a field hospital after an alleged chemical attack in Idlib, northen Syria
Theresa May spoke with US President, Donald Trump, during a phone call on Monday, about the crisis in Syria and they both agreed a "window of opportunity now exists" to persuade Putin, to cut ties with Syria.
Speaking about Mrs May’s earlier phone call to Trump, a Downing Street spokesman said: "The President thanked the Prime Minister for her support in the wake of last week's US military action against the Assad regime.
"The Prime Minister and the president agreed that a window of opportunity now exists in which to persuade Russia that its alliance with Assad is no longer in its strategic interest.
"They agreed that US Secretary of State [Rex] Tillerson's visit to Moscow this week provides an opportunity to make progress towards a solution which will deliver a lasting political settlement."
Countries that support and oppose the missile strikes in Syria
Mon, April 10, 2017
European countries have been broadly supportive so far as President Trump ordered missile strikes against a Syrian airfield from which a deadly chemical weapons attack was launched
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SYRIA OPPOSES: President Bashar al-Assad's office denounced the U.S. strike as 'reckless, irresponsible behavior.'
A Whitehall source earlier hinted that Russia may be encouraged to withdraw from Syria with the prospect of being able to rejoin the world’s leading G7 group, which is understood to be desired by Mr Putin after he was suspended from the forum in 2014.
Mr Tillerson landed in Moscow to deliver the G7’s message on Tuesday night, saying that the Russian president can either help solve the Syrian crisis or share Mr Assad’s legacy of destruction.
He added that Russia had either been "incompetent" or failed to take its obligations over chemical weapons seriously, but distinction "doesn't much matter to the dead”.
Mr Trump’s son Eric has also said that his father will not be intimidated by Mr Putin.