Johnson has come under fire in recent weeks, with Posh losing 3-0 to Brighton at London Road recently as well.
With the club having three different managers last season, many believed MacAnthony was set to wield the axe again.
But he told BBC Radio Cambridgeshire: "I don't need to give him a vote of confidence. I made a lot of mistakes last season and the last thing I'm going to do is start pressing the panic button.
"However, I feel we need to remain a little bit calm. I know people are getting a little bit antsy about what's going on, and after two defeats like that they've got every right to be antsy."
Johnson's men will be looking to put things right against Stockport in their FA Cup replay on Tuesday night before facing a tricky trip to Southampton on Saturday.
Source: PA
Source: PA