Posh return to the second tier of English football on the back of successive promotions under Darren Ferguson.
And MacAnthony insists that momentum will prove to be a huge advantage for his young, vibrant side.
MacAnthony told the Peterborough Evening Telegraph: "We have something not a lot of teams have and that is two years of momentum and success achieved by players who have yet to reach their peak.
"I feel we will shock the football world and compete at the top end of the Championship this season. Our club has nothing to fear and hopefully we will play the same style of attacking football and let other teams worry about us and not worry about them.
"It's going to be a massive season for all of us and an enjoyable one. Of course the league is full of the so-called big boys, but history tells us teams like Wigan, Reading, Hull and, of course, Burnley can buck the trend and get to the promised land."