The Blues are currently languishing in 17th place in the Premier League, just a solitary point above the drop zone.
They have picked up just one victory from their eight fixtures to date and have tasted defeat in three of their last four.
That alarming slump has given cause for concern for all those connected with the St Andrews club, with Saturday's home date with Blackpool being billed as a must-win fixture.
But centre-half Johnson claims no-one is considering the prospect of relegation.
"Of course we're concerned," he told the Birmingham Mail. "Eight games in, it is early. But games will tick away if we don't start picking up results.
"The target for every Premier League team in our position is a point a game, and we're below that at the minute.
"It's not gone for us, we're lacking goals. Nikola Zigic got his first one (against Arsenal on Saturday), that's great, and hopefully he will kick on now and get a few more.
"We have made some bad errors, we've been getting some bad decisions against us, which aren't helping, a bit of bad luck with own goals and stuff and penalty decisions.
"When we are conceding goals, apart from the West Brom game, we're not getting opened up. We are still quite solid defensively.
"It's just in that final third we don't seem to be getting the goals ourselves.
"Yes, of course, Blackpool is now important. We're at home, we need to win the game. We have to win the game. Simple.
"But there's no panic at all. We're far too good to go down. There's enough belief in that dressing room. We've got some great players, a good squad and relegation is not even in our minds."