Following Saturday's 1-1 draw at home to 10-man Stoke, in which Johnson put Norwich in front with an early second-half header, Chris Hughton's side are four points clear of the bottom three but face a daunting run of fixtures at the end of the season.
In their final four games, Norwich take on title challengers Liverpool, Chelsea and Arsenal, as well as reigning champions Manchester United, but it is the matches before then that Johnson is keen for the club to stamp their authority on.
After next weekend's trip to Southampton, the Norfolk club have a quartet of matches they will be targeting points from as they take on Sunderland, Swansea, West Brom and Fulham.
In recent times Norwich held previously free-scoring Manchester City to a goalless draw and recorded a 1-0 win over Champions League-chasing Tottenham.
Those kinds of performances are what Johnson knows need to be replicated in the coming weeks.
"We turn it on when we play the big teams," he said.
"We need to do the business when we play the teams in and around us. That is something we have been working on off the pitch, we can't just raise our game when we play the big teams, we have to do it for every game we go in to.
"We have got some home games to play and we are playing teams in and around us soon, so hopefully we can pick up some points.
"We are not setting a target, we just want to win as many games as we can. We are good at home and we go away to Southampton on Saturday and will hopefully pick up points there."
Johnson's opener against Stoke was cancelled out by a Jon Walters penalty, although the ex-Ipswich forward was shown a red card less than five minutes later after catching Alex Tettey with a high challenge.
Johnson looked to take the positives from the draw and felt Stoke defended well once they were reduced to 10 men.
"We are a point closer to where we want to be, which is staying in this league," he said.
"We can take positives out of the game but we are disappointed we didn't get all three points.
"It was hard for us, with them going down to 10 men they got everyone behind the ball.
"They are a big physical team and are good at heading the ball. They sit there and want you to break them down, they are well-organised and when you go down to 10 men you work that extra little bit harder."
Stoke captain Ryan Shawcross was happy to head away from Carrow Road with a point, although the draw means Mark Hughes' side have not won on the road in the Premier League since August.
"It is a very good point, it is a tough place to come," said Shawcross.
"They have beaten some very good teams so, given the circumstances, it is a good point. We have had a few blips but overall we are pleased with the performances away from home. Any point away from home is pleasing."