Johnson, who is due to leave office next month, spoke at a joint news conference with Ukrainian President Volodymyr Zelenskiy on his fourth trip to Ukraine this year as Ukraine celebrated 31 years of independence from the Soviet Union.
Johnson, whom Zelenskiy described as his "dear friend Boris," said it was vital that Europe keep up its military and economic support for Ukraine even as rising energy and food prices were causing some consumers pain.
"We also know that if we're paying in our energy bills for the evils of Vladimir Putin, the people of Ukraine are paying in their blood," Johnson said.
"And that's why we know we must stay the course. Because if Putin were to succeed, then no country on Russia's perimeter would be safe, and... (that) would be a green light for every autocrat in the world that borders could be changed by force."
Johnson's trip coincided with the six-month anniversary of what Russia calls its special military operation.
It came amid fears that Russia could again launch missiles at major cities in Ukraine to cast a pall over Ukrainian Independence Day.
Air raid sirens sounded several times in Kyiv on Wednesday.
Johnson is due to leave office in less than two weeks, but the two candidates to replace him, Foreign Secretary Liz Truss and former finance minister Rishi Sunak, have both pledged to continue the UK's support for Ukraine.
The outgoing UK leader warned against "any creeping attempt to normalise relations with Putin," especially given growing signs that the Russia offensive was failing and that Putin was racking up what he called colossal losses.
"This is not the time to advance some flimsy plan for negotiation with someone who is simply not interested. You can't negotiate with a bear while it's eating your leg," he said.
His comments came days after Turkish President Tayyip Erdogan urged Zelenskiy to consider fresh negotiations with Putin on ending the war, building on the positive momentum of a UN-brokered grain export deal.
"To all our friends, I simply say this, we must keep going. We must show as friends of Ukraine that we have the same strategic endurance as the people of Ukraine," Johnson said.
Johnson has been among Ukraine's most vocal backers during the war.
Zelenskiy said it was vital Ukraine and its allies did not allow Russia to seize the momentum in the war.
"We cannot relax, we cannot freeze the conflict, we cannot wait a year, or two, or three... We cannot, under any circumstances, give up the initiative," Zelenskiy said.
The Ukrainian leader thanked Johnson for "the uncompromising support for our country from the first days of the full-scale Russian aggression".
In an emotional speech to his compatriots earlier on Wednesday, Zelenskiy said Russia's attack had revived the country's spirit.
"A new nation appeared in the world on February 24 at 4 in the morning. It was not born, but reborn. A nation that did not cry, scream or take fright. One that did not flee. Did not give up. And did not forget," he said.
The 44-year-old leader, speaking in front of Kyiv's central monument to independence in his trademark combat fatigues, vowed to recapture Russian-occupied areas of eastern Ukraine as well as the Crimean peninsula, which Russia annexed in 2014.
