Johnson expressed his satisfaction with aspects of his team's work, particularly at the breakdown, but warned that there was much work to do ahead of the next match, against Ireland in a fortnight's time.
He said: "We can't be chimneys, you know, and keep blowing smoke where it shouldn't be. We've got to acknowledge that we've got to keep improving. We're in a tournament here. And today's result puts us right in it. We acknowledge the good, yes, enjoy the good, but we come back and start again."
Johnson identified Stuart Hogg's 47th-minute interception try as the defining moment of the game, coming as it did just as Italy, trailing 20-3, were threatening the Scotland line. However, he also pointed out that the Scots had left themselves open in the moments before that score.
"We did really well in defence for most of the game," said Johnson. "There was a really key moment in the game when Hoggy took it from end of the field to the other. That's a 14-point turnaround, but what occurred before that was disappointing.
"That scoreboard can switch pretty quickly. I keep saying that if we keep getting our part right we can put teams away because we've got a potent backline and we've got ability to put sides away."
With France going down to a shock 16-6 loss to Wales in Cardiff yesterday, the Six Nations is already shaping up as the most open in years. France, who lost to Italy last weekend, are the only team without a victory, and all five other teams are now on two points. Scotland hold third place on points difference, but they could move up a slot if Ireland – or even England – suffer a heavy defeat in Dublin today.
Johnson backed Ireland to win, a scenario that would mean they would come to Edinburgh in two weeks' time believing they could be on their way to a Grand Slam. Again, the coach emphasised that Scotland's next game will be another step up.
"There were parts of the game where we showed we can score points and put pressure on the opposition, and that's good," he said. "But there has to be honesty again. Sometimes the scoreboard hides some ills and we'll be honest about it.
"There was some really good stuff and Ireland will be another step up. I have a feeling they'll get over the line against England and they will be coming here looking for a championship. But it's in our own hands now and that's a pretty good place to be."
Kelly Brown, who claimed his first victory as Scotland captain after four straight defeats, said he was proud of the efforts of his players, particularly in the way they addressed the flaws that had been exposed by England.
Brown said: "We felt last week that England won all the one-on-ones, but I felt that out there we fought and grafted and my over-riding emotion is probably one of pride. We needed to bounce back and I think we did that. But it's only the start, only one game and it's up to us to make sure that we learn from this match and on our next outing we are even stronger."
Scotland also came through the game relatively unscathed, with the only worry being prop Ryan Grant, who took a knock early in the game but played on until the 59th minute.
"Ryan was in a lot of pain very early in the game," said Johnson of the player. "A lot of pain. And he toughed it out against a really formidable pack. It just says so much about the person."