The former PM, who now sits as a backbench MP, said any deal with Russian President Vladimir Putin would “send a signal around the world that violence does pay off”.
“There is absolutely no sign that Putin either wants such a compromise or can be trusted to deliver it,” he added.
“That is why we have absolutely no choice but to stay the course – to stay resolute.
“If Putin is going to double down on his aggression we must double down in our defence of the Ukrainians.”
Supporting Ukraine was a key policy plank of Mr Johnson’s premiership. He was a close ally of Ukrainian President Volodymyr Zelensky, visiting Ukraine three times since it was invaded seven months ago.
On his final visit to Ukraine last month, Mr Johnson said the West must endure rising energy bills to help the country drive out Russia.
Mr Johnson admitted rising energy prices meant “times are tough for families”, during a debate in the House of Commons on the situation in Ukraine on Thursday.
But, he argued, the UK has “the economic muscle” to help families with fuel bills, as well as secure an independent energy supply through the use of “more nuclear and much more wind”.
Earlier this month Ukrainian forces have pushed back Russian troops, retaking more than 6,000 sq km (2,317 sq miles) in the space of two weeks.
“It is more vital than ever that we have the strategic patience to hold our nerve and ensure that the Ukrainians succeed in recapturing their territory,” he said.