After rejecting what Town chairman John Fenty called a "derisory" first offer from Peterborough, the Mariners then turned down a much-improved second bid for the 19-year-old defender from the Championship newcomers.
MacAnthony told the Peterborough Evening Telegraph: "I am gutted at missing targets, but it wasn't for the want of trying. We missed out on Bennett which annoyed me big time as we put together a deal that would have earned Grimsby up to a million over time.
"I am sure it would have allowed them to bring in four or five good players that may have given them a good push in League Two.
"I can appreciate when a club doesn't want to sell its best assets and that is fine if you are already competing at the top end of a league, but it may not be too prudent when you need to improve your squad."