Ferguson, who guided Posh to two successive promotions, made an acrimonious exit in November and received a good reception from home fans, but he followed up his first success as North End boss by slamming claims from MacAnthony that he had been guilty of unsettling Posh players since leaving the club.
"I'm not happy about what was said and have to defend myself against allegations of tapping up the Peterborough players and other items," said Ferguson.
"I got the club into the Championship for the second time in 75 years and we should just leave it like that.
"It seems like they are trying to ruin my reputation. I wish I didn't have to talk about those comments but I'm sure people appreciate my need to give my reaction.
"It is obviously to get my first win as Preston manager. It is always important to get the first one on the board.
"I hope Posh stay up for the fans, the players and their manager Mark Cooper, but it will be hard for them."
MacAnthony himself was not at the game due to a business trip in the United States, and he missed a dour battle.
Michael Hart had a shot scrambled away in the first minute before Preston found themselves on the receiving end of a full 30 minutes of home pressure, surviving thanks smart saves from Andy Lonergan and poor finishing.
Lonergan held a header from transfer listed Aaron Mclean, in his first start of the year, and pushed away a 20-yard drive from Josh Simpson, with Chris Brown clearing Charlie Lee's snap-shot from a resulting corner.
Chris Whelpdale twice blazed over and Simpson fared no better before Mellor broke the deadlock with a 34th-minute left-footed effort into the top corner from Ross Wallace's square pass after picking up a poor clearance from Kerrea Gilbert.
Posh's Joe Lewis was the busier goalkeeper as the second period opened producing a superb reflex save to tip over Richard Chaplow's close-range header.
Lewis held on to a shot from one-time Posh defender Sean St Ledger and then Mellor was close to a second with one effort punched out by Lewis before a second shot was cleared off the goal-line by Ryan Bennett.
Ferguson was full of praise for his Preston side and especially scorer Mellor.
"Neil did really in a different role not staying really wide and took his goal well. Overall the players deserve a lot of respect as it was never going to be an easy place to come with Peterborough fighting for their lives," he said.
Bottom side Posh rarely pushed forward with any real conviction apart from a late break by George Boyd, whose low 25-yarder had Lonegran at full stretch to hold the ball at the second attempt.
It was another frustrating display for manager Mark Cooper, who commented: "Once again I can't question the players' commitment but after getting loads of bits and bobs around their box we lacked the quality to make the most of them.
"We just have to do the best we can with what's available, although after getting a couple of players out on loan it gives me a little more scope."
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