"I liked our intent," he told BBC Sport. "From the start, we were competitive at the contact, we turned the ball over early and were rewarded.
"I keep saying it, if we get that part right, we can finish sides off. We showed that today.
"It wasn't perfect, we acknowledge that, but there were pleasing signs and we showed good skill to finish."
Stuart Hogg's 80-metre scoring sprint was the highlight of a four-try display from Scotland at Murrayfield against a side that had beaten France the previous weekend.
Laidlaw lauds "brilliant" win
Hogg's fabulous solo counter-attack followed Tim Visser's fifth try in seven internationals and Matt Scott's first, while Sean Lamont added another breakaway score.
Scrum-half Greig Laidlaw produced a perfect kicking display for the rest of the home points before Alessandro Zanni got a late consolation try.
Johnson had only made two changes from the team that lost 38-18 at Twickenham, both of them enforced with hooker Ross Ford and flanker Robert Harley, making his first Scotland start, replacing the injured Dougie Hall and Alasdair Strokosch.
And the Australian coach's selection was vindicated as the Scots responded with a display full of vim and vigour.
"No one can ever question the passion of the side, the integrity of this team is great, that goes without saying," explained Johnson on BBC Radio Scotland.
"But passion will only get you so far; you need to finish your skill-set off.
"There was a 14-point turnaround when Hoggy intercepted.
"That's the beauty of the side, we can punish teams when they falter because we can go the full length, we've shown that in the last two weeks against quality opposition.
"We've got speed to burn and some quality, we've just got to keep doing it.
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"We're back in this tournament. We're in it up to our eyeballs!
"Ireland will be here in two weeks and they will be ready to play. This will count for nothing if we don't get the next part right.
"Instead of worrying about the woes of last week we can worry about winning the tournament."
Laidlaw was named man-of-the match but was quick to heap praise on Scotland's forwards.
The scrum-half also said the victory was for the fans at Murrayfield who had not witnessed a home win since the warm-up Tests ahead of the 2011 World Cup.
"Absolutely brilliant," Laidlaw told BBC Sport. "There have been tough times for fans - this one's for them.
"We had to do the dirty work. I'm fortunate enough to pick up the man-of-the-match but that's because the forwards did their job."
Laidlaw, who played at fly-half in last season's tournament, did much to control the game and Johnson was very pleased with the 27-year-old's contribution.
"Greig Laidlaw is a wonderful lad but a wonderful technician," he explained.
"He knows he is not the most gifted athlete but he's so much quicker with the ball - his mind works faster than opposing players."
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