The Dark Blues boss will lead his side to Rome this weekend ahead of a potential RBS 6 Nations wooden spoon decider against Italy.
It comes after two dismal defeats to Ireland and England in which the Scots have conceded almost 50 points and scored just six.
The humiliating 20-0 loss to the Auld Enemy at Murrayfield a fortnight ago - the first time the Scots had failed to trouble the scoreboard against their neighbours since 1978 - has in particular sparked a furious backlash from fans and former players.
Peter Wright, the 21-time capped prop, labelled Johnson a "joker" after the defeat while ex-England coach Sir Clive Woodward claimed his side would struggle to beat any of the 12 sides playing in the Aviva Premiership south of the border.
Asked about the criticism, though, Johnson said: "I haven't given it a second thought to be honest. All I care about is the team - did we perform well? We didn't. Should we be disappointed? Yes we should.
"It's amazing - the people that judge you the most know you the least. I am happy with who I am. I ain't changing. And I don't really care what they say about me.
"Everyone is entitled to their opinion, I'm not going to hold it against them. The people I care about are the people that are close to us."
However Johnson - who opted against rolling out any of his trademark wisecracks and one-liners as he faced the media - did admit his team must start performing better.
Asked about Woodward's brutal assessment of his team's display, he responded: "I didn't know he had said it but at the end of the day, we have got to do better. The best way to close critics' mouths is to perform."
Johnson has made three changes to the pack taken apart by the English for the Azzurri clash, including a recall for lock Richie Gray .
The British and Irish Lion was only used as a second-half substitute in the Championship opener against Ireland before he was dropped completely ahead of England's arrival in Edinburgh.
But the Castres forward will replace Tim Swinson in Rome, while out-of-form hooker Ross Ford also switches to the bench as Newcastle's Scott Lawson comes in.
And number eight David Denton loses his place to Johnnie Beattie despite being the only Scot to have impressed so far.
But Johnson said the Edinburgh man is not yet the finished article.
"There is a lot that we like about Dave with the ball, but it's not the same without it," said the Australian. "We want the same energy from him with and without the ball."
Ford was lucky to keep his place for the Calcutta Cup meeting after an erratic display at the line-out in Dublin but fared even worse back at Murrayfield.
"A guy that has been around as long as he has knows [that he isn't playing well]," said Johnson. "The simple truth is that he just needs to execute it better.
"He needs to go back to the training ground. Practice makes perfect as they say."
Gray's omission two weeks ago raised eyebrows but Johnson insists even the 6ft 10ins giant cannot expect to stride straight into his line-up.
He said: "I don't want it to be a given that you can play for Scotland. I want people to play for Scotland on achievement and form.
"Richie has acknowledged that and has worked on a couple of things. He's a great lad and it's nice to have him back."
However, skipper Kelly Brown has again been overlooked, with Chris Fusaro starting at number seven and Greig Laidlaw chosen to lead the Scots out at the Stadio Olimpico.
But Johnson insists the Saracens flanker's international career is not over.
He said: "Kelly is there or thereabouts. It was a tough decision for me personally because he's a lad I really like. I respect him enormously.
"I spoke to Kelly last night. He needs to learn to be a bit more aggressive at seven but he will do that.
"He's not lost to Scottish rugby. We have a good battle for spots and that's what you want."