Peterborough frustrated their hosts for 90 minutes before conceding a last-minute goal and MacAnthony was furious that Posh gave Brighton "too much respect".
MacAnthony tweeted: "Some words to describe that and my day in general: Pathetic, boring, negative, lacklustre, irritating. Not a happy man after that.
"Brighton haven't had the best home form and would have been nervous. We have enough offensively to hurt anyone.
"It would have been a travesty if Brighton hadn't won as they played to win! gave them too much respect. After our home wins that baffles me."
The defeat left Peterborough in the bottom three while Brighton rose to eighth.