The 40-year-old joined Twitter in 2011 and often interacts with fans through his personal account.
"They have no clue how to run a football club," MacAnthony told BBC Radio Cambridgeshire.
"No disrespect to them, yes they buy a season ticket, but they're not in a position where they have to make a decision that affects people's lives."
He continued: "You're talking about the hundreds of people who work for you, you're talking about the family of the player, you're talking about the player himself, the after-effect if you don't do business.
"It's all about how you handle that, I've always felt I've got that right."
MacAnthony, who is celebrating 10 years as Posh chairman, has been most hurt by criticism of his transfer policy, with fans often accusing him of selling the club's best players.
"I was getting it last year with Conor Washington, they were hammering him, he was one of my favourite players and I thought he would come good," said MacAnthony.
"When I got £2.8m from QPR for him I felt like tweeting a picture of the agreement and going with two fingers to all the people who had, non-stop, had a go.
"In other words: 'I know what I'm doing, back off, if you think you know what you're doing go buy a football club.'"
Despite his public run-ins with angry fans on social media, MacAnthony has no plans to delete his account.
"Winners never quit, quitters never win," he said. "I wouldn't change it, I love it, it's great fun. You do get trolled, you do get hammered, there are the ups and the downs."
And MacAnthony has reiterated his pledge to secure promotion from League One this season.
"I'm giving it everything this season," he added. "We're going up, there is no tomorrow, it has to be now and it has to be this season.
"You could say that puts a lot of pressure on the players and the manager, they're all aware, they know what they need to do. It's time to stand up and be counted, let's get out of this league.
"There is no looking back for me after this season. I'm only talking about Championship football."
Listen to an extended interview with Darragh MacAnthony via the BBC iPlayer.
Peterborough United chairman Darragh MacAnthony has spoken about supporters who criticise his running of the club.