Martin O'Neill's side have been dragged into the relegation battle following a run of seven matches without a win and are now just four points clear of the drop zone.
They will attempt to bounce back after the international break but face a tough challenge at home to Premier League leaders Manchester United.
However, Johnson insists everyone at the club will keep a positive mindset, saying in The Sun: "You have to come in and move forward rather than dwelling on any disappointment you might just have had.
"If you let bad results affect you going into your next game, you'd be lost.
"We've just got to get ourselves together again, train hard for the next couple of weeks and then go into the big game.
"We know we have to do better. It's back to the drawing board."
Johnson feels confident that Sunderland will soon rediscover top form, even though their clash with United is followed by a trip to Chelsea.
He added: "When things aren't going well, people get down - the team, the fans, everything - it's part of the game.
"A couple of good wins, though, and it changes very quickly and everyone's happy again.
"When it goes bad, it can seem that there's no way out, but we've got a couple of important games coming up and it's important not to dwell on what we should have done previously."