Blues have drawn 11 of their Barclays Premier League matches - the highest number in the division alongside Fulham - and are hovering above the bottom three.
Johnson knows successive matches against West Ham, Stoke, Newcastle, Everton and Wigan in the next month will have a major impact on their chances of avoiding the drop.
The central defender told Press Association Sport: "I'd rather win two and lose two than all these draws.
"Draws are okay but they are not going to get you up the league.
"We are still in that basement battle and only picking up three points from matches is going to get us out of that."