He told BBC Radio Cambridgeshire: "I'd like people to be sending letters into me rather than the newspaper, then maybe I'll have a cup of tea with them.
"I'm always available. But it's got to be their proper name, not a pseudonym."
After losing 5-1 to Charlton and 4-1 to Southampton Posh are showing signs of having turned a corner with a point against Leyton Orient and an FA Cup win at Bury.
But Johnson knows his side, having slipped to 10th in League One, will face criticism after failing to live up to their billing as pre-season title contenders.
"Sometimes it's not unwarranted and we criticise ourselves just the same," he said.
"But when you support a football team you have to support them properly, right through the season, and you can have your little moan now and again when the lads haven't played well.
"But at the same time you're supporting that team and manager and chairman and director of football for the period that they're there.
"We know we're not out of it yet, we had two really poor games on the trot but we certainly have not, overnight, become a terrible team and I for one know that we'll be back up there."
With Saturday's trip to Johnson's former club Yeovil called off, Posh are next in action against Rochdale on Friday, 10 December.
Source: BBC Sport
Source: BBC Sport