MacAnthony was responding to criticism aimed at the Sky Bet League One club after wantaway striker Lee Tomlin was denied the chance to move to Scottish champions Celtic, who have been drawn against Barcelona, AC Milan and Ajax in the Champions League.
The Hoops saw three bids for Tomlin, who last month submitted a transfer request, rejected by Peterborough last Saturday.
Posh were incensed that the offers - the highest of which was thought to be B£2.1million - arrived on the day of, and during, their league game against Crawley.
Tomlin was made aware of the bids and the 24-year-old's performance suffered as a result and he was substituted at half-time.
MacAnthony said via his Twitter account: "I won't let our club be bullied. We don't give our players away and I want us to win the league.
"I used to be a Celtic fan, but not any more!"
Tomlin excelled in the Championship last season and has scored six goals in the first six games of the current campaign.