Mr Tugendhat had backed Michael Gove in the Conservative Party leadership contest, which will also decide the next occupant of No 10 Downing Street.
Mr Johnson polled 160 votes among his fellow MPs last week, while Jeremy Hunt picked up 77, edging out Mr Gove on 75 for the final showdown.
In his role as chairman of the Commons Foreign Affairs Committee, Mr Tugendhat had already crossed swords with Mr Johnson in his days as Foreign Secretary.
Mr Tugendhat, who has himself been tipped for the top job, worked as a military assistant to the Chief of Defence Staff before he was elected in the borough in 2015.
A veteran of campaigns in Afghanistan and Iraq, he was also an intelligence officer attached to the Royal Marines.
‘This is not a game, this is really not a game when you take over in No 10. There is nobody, literally nobody, to second-guess you’
In a Huffington Post Commons podcast he recalled the decisions he had had to ask the Prime Minister to make.
“A number of times we’d go over to No 10 with a brief and it was an urgent decision as to whether or not to launch a helicopter with 12 men in it to go and rescue a hostage,” he said.
“If you make the wrong call there, you may not only be leading to the death of a single hostage, you may be killing all those 12 men and the two pilots because you’re not over the detail.
“This is not a game, this is really not a game when you take over in No 10.
“There is nobody, literally nobody, to second-guess you. The decision stops with you. There isn’t an appeals process, there isn’t a further decision.”
In reference to his previous support for the Environment Minister Mr Gove, he said: “That’s why I went for someone who I think is a leader and can actually make those decisions.”
Mr Gove was eliminated in the final round of voting by Tory MPs last week, leaving only the current Foreign Secretary, Mr Hunt, up against the runaway favourite Mr Johnson.
The vote to decide the winner will now be made by 160,000 Conservative Party members, with an announcement to be made on July 23.
Mr Tugendhat’s comments refer back to another dig he made at Mr Johnson when the latter was Foreign Secretary in 2017.
The leading candidate is prone to making off-the-cuff and inappropriate remarks, and Mr Tugendhat said: “It is really, really hard to do cross-cultural humour.”
Mr Johnson resigned last July in protest at Theresa May’s ‘Chequers’ deal to deliver Brexit.
‘I’m looking forward to hearing more about their vision for the country to address the issues we all face’
A month later, he wrote a column in the Daily Telegraph in which he described Muslim women wearing niqab face veils as looking like ‘letterboxes’ and ‘bank robbers’.
The candidate has also been criticised for failing to get his facts right. He was forced to apologise after a gaffe about British-Iranian mother Nazanin Zaghari-Ratcliffe, who was imprisoned in Iraq on charges of spying while on holiday.
He told the Foreign Affairs Committee she had been teaching journalism. Mrs Nazanin Zaghari-Ratcliffe’s family said the Iranian authorities had seized on the error to build evidence against her.
Last week her husband Richard Ratcliffe said: “Johnson’s failure to take responsibility for his own mistakes makes me question his ability to protect our security.”
Mr Ratcliffe has gone on hunger strike outside the Iranian embassy in London to protest against his wife’s continued detention.
In the Commons yesterday [Tuesday], Mr Hunt called on Iran ‘let her come home’.
Mr Tugendhat, who will be at the forefront of dealings with European leaders after Brexit, told the Times: “I voted for Michael Gove in the Parliamentary rounds but unfortunately he didn’t make it to the final two candidates.
“I’ll be listening to everything Jeremy Hunt and Boris Johnson have to say. Of course, I now have just the same vote as every other Conservative Party member and like many members I’ve spoken to, before casting my vote I’m looking forward to hearing more about their vision for the country to address the issues we all face.”