MacAnthony 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."
Darren Ferguson, Mark Cooper and Jim Gannon all fell by the wayside at London Road last term as Peterborough were relegated from the Championship.
Johnson took hold of the reins with four games remaining at the end of the 2009-10 campaign and was duly given funds by MacAnthony to build a side capable of winning the League One title.
Posh sit eighth in the table after 16 games and are just three points adrift of an automatic promotion place.
But Saturday's 5-1 reverse at home to Charlton and the 3-0 defeat by Brighton at London Road two weeks earlier
left Johnson questioning his ability
to take the side forward.
"I think Gary plays a bit of kidology, reverse psychology to try and psych his players up," explained MacAnthony.
"He's very happy with the squad he's got. The players know they've let us down, we don't need to be on top of them even more and make it worse than it is.
"Does it hurt when we lose 5-1 when I'm watching? Of course it does.
The manager's job is not being helped by a team that look frankly gutless at the moment
KryptonC07
"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.
"But we've got to support the boys and the manager. He's got a 50% win ratio, so before we start throwing him out and feeding him to the lions, let's calm down and remember where we were at the end of last season."
Posh host Stockport on Tuesday in an FA Cup first round replay, with the winners going on to face Bury.
Source: BBC Sport
Source: BBC Sport