"You always question everything when you lose - whether the training was right, whether your lunch was right, whatever it may be," he said.
"People need to show me whether or not they're up for this because I'm up for this."
Posh remain just three points off the automatic promotion places in League One, despite having lost four of their last six matches.
Johnson believes it will take time to turn the club's fortunes around after a season of struggle in the Championship.
"Fans need to trust the management, trust the chairman, trust [director of football] Barry Fry and see where we end up," he said.
But he also warned his players that a major improvement is needed over the coming weeks.
"Ultimately it's about the players out on the pitch because we know those players can play, but on occasions this season we have looked poor," he said.
"If I have 14 people asking for a transfer tomorrow then I'll have to look at myself, but otherwise we need to stay strong."
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