They are well on course to secure a top-half finish, while European qualification is still not out of the question.
With plenty still to play for heading into the final few weeks of the season, Johnson claims Blues have no intention of allowing all their hard work to go to waste.
"I am sure that has happened before at other clubs, you get yourself safe and then take your foot off the gas," the commanding centre-half told Sky Sports News.
"But that's not what we are like and we will look to put things right on Wednesday because we were disappointed with the way we have performed in the last two games."
Birmingham head to Blackburn in midweek looking to bounce back from below-par performances against Everton and Sunderland.
Alex McLeish's side shipped early goals in both of those games, leaving them with just a solitary point to show for their efforts.
Title-chasing Arsenal are then due at St Andrew's on Saturday and Johnson believes the Blues should be looking to take something from each of their next two fixtures.
"We go into every game wanting to win it, not looking at drawing," he said.
"Arsenal won't fancy coming to us at the weekend, they have got a few players out, and we are decent at home - we have only lost two games at home."
Blackburn v Birmingham. Click here to bet.