The 2019-20 term in Leagues One and Two were curtailed in June this year amid the Covid-19 pandemic.
The final table was determined on a points-per-game method which shifted Posh out of the playoffs, which were then played behind closed doors.
The rapid rise in coronavirus cases and a raft of postponements throughout the English Football League has led to concerns in some quarters that the current campaign could be similarly affected.
But MacAnthony, whose side are currently fifth despite a run of game postponements due to Covid, told Sky Sports: “I think the season will finish. We don’t need to go to those headlines again.
“I think that was last year’s headline and, going in to 2021, look, we’ve got until the start of May to finish our season.
“If we have go to the end of May, so be it. League One and League Two are not going to have many players going to the Euros this summer.
“So I don’t see why we can’t go an extra two or three weeks if necessary.”
West Brom manager Sam Allardyce has voiced support for a “circuit break” in the Premier League as the number of positive coronavirus tests continued to rise.
A report in The Daily Telegraph said representatives of some top-flight clubs had proposed a two-week ‘cooling off’ period, and Allardyce insisted it was the “right thing” to cope with the outbreak.
MacAnthony, however, questioned whether the 66-year-old former England manager should be working alongside young athletes given that the older age group are at greater risk of the consequences of coronavirus.
“I understand where Sam Allardyce is coming from, this really affects people badly who are over the age of 60,” MacAnthony said.
“If I was over 60 I’m not sure I’d want to work in a job surrounded by young people, who could potentially have the virus and are going out or staying in as they should be.
“That’s no derogatory comment to footballers, I’m just surprised Sam took the job. If I’m over 60 I wouldn’t be taking a job in football until I’m vaccinated in the next couple of months.
“There’s no point in coming in now and saying we should have a circuit break and stop for two weeks.
“Football has done this well really. I think they’ll continue to do this really well, we’ll get over this bump into January and get this show back on the road.”
The Premier League this week returned its highest number of positive tests this season.
Between December 21 and 27, the League tested 1,479 players and club staff and 18 tested positive, eclipsing the previous highest number of cases – 16 in the week of November 9-15.
Manchester City began retesting their squad on Tuesday, hoping to have prevented a wider outbreak after Monday’s postponement at Everton.
Nine games across the Sky Bet Championship, League One and League Two on Tuesday were postponed because of the virus, while Rotherham boss Paul Warne said his side are only playing their match with Barnsley to avoid a possible points deduction by the EFL.
Rochdale are one of the clubs in League One whose next two games have been postponed and their club doctor Wes Tensel called for the EFL to see the “bigger picture” and halt the current campaign.
Tensel, who is also a practising GP, told the PA news agency: “This is my opinion as a doctor. Some people will disagree, some won’t.
“This is just my opinion based on what I have seen working in the NHS and at a football club.”