Ferguson questioned referee Alan Wiley's fitness after Manchester United's 2-2 draw with Sunderland, while Allardyce criticised Peter Walton for not giving a penalty for Thomas Vermaelen's apparent trip on David Dunn in Blackburn's 6-2 defeat at Arsenal.
A spokesman for the FA said: "We are reviewing the comments in their full context."
Ferguson said after the draw at Old Trafford that 49-year-old Wiley was struggling to keep up with the match.
"I was disappointed with the referee," Ferguson said. "He didn't add on any time for the goal. He played four minutes and two seconds.
"He was also walking up the pitch for the second goal needing a rest. He was not fit enough for a game of that standard.
"The pace of the game demanded a referee who was fit. He was not fit. It is an indictment of our game.
"You see referees abroad who are as fit as butcher's dogs. We have some who are fit. He wasn't fit.
"He was taking 30 seconds to book a player. He was needing a rest. It was ridiculous."
Professionals union Prospect, who represent referees, have defended Riley, describing Ferguson's comments as "totally unwarranted".
Alan Leighton, the national secretary of Prospect, told Sky Sports News: "The referees never want to be the centre of attention in games and it is disappointing that yet again they are put in that position.
"My main concern is about the unfounded and totally unwarranted remarks about Alan Wiley's fitness
"Not only does it dig at the heart of Alan's professionalism where he is one of our top and longest-serving referees, but it also has an impact on all the others.
"I understand that Sir Alex made comments about other referees and said about European referees being fit as butchers' dogs, comparing them with some referees from the UK who aren't fit.
"All of the referees, all of the officials and all of the assistant referees pass stringent fitness tests at the start of the season.
"Prozone statistics are used to monitor their performance in every game. If Alan Wiley or any other referee were not fit they would not be refereeing."
Former Premier League referee Dermot Gallagher - a close friend of Wiley - said referees were now just as professional as the players.
"In the 17 years the Premier League has been going this is the first time I have ever heard a manager use that criticism of a referee," Gallagher told Sky Sports News.
"I hear all kinds of things and I have never known a manager to say a referee wasn't fit enough. In the year 2009 with the training they have got now, it's the most ridiculous comment I have ever heard.
"The referees are fit for purpose. They are training four, five, six times a week. They are training to an intensity which 10 years ago I would never have believed and they are monitored on a daily basis by sports scientists.
"Everything is so scientific - referees now are very akin to players in their professionalism.
"Alan Wiley was my room-mate for nine years and he is the most competitive guy I have ever met in my life.
"I used to think I was one of the fittest referees and if he thought I could run a yard further than him in training it would break his heart, honestly. He really is the consummate professional.
"It is quite astonishing - of all the referees that someone could label with this criticism, it really is the wrong one."
Ferguson has frequently courted controversy for his comments about referees over the years.
He was warned about his conduct in 2008 after criticising referee Martin Atkinson for failing to give United a penalty in the FA Cup quarter-final defeat to Portsmouth.
And in 2007 he questioned Phil Dowd's competence after the referee sent off Paul Scholes and Wayne Rooney
in United's 2-0 Premier League defeat at Fulham.
Blackburn boss Allardyce could be in trouble after he questioned whether Walton was good enough to referee in the top flight after turning down a Rovers penalty claim at the Emirates Stadium.
"I don't want to detract from Arsenal but it was a blatant penalty," Allardyce said. "There is no doubt in my mind that the position of the referee was excellent.
"He just didn't, unfortunately, give the decision in our favour.
"It is human beings in a very big pressure position.
"In the big pressure pot that is this league, you have got to get the major decisions right otherwise you don't stay in this league too long, not as a manager or a player, so as a referee you have got to be judged the same.
"They are fully professional now so if they are not good enough, we should find someone who is.
"That decision wasn't good enough for me and it had a major effect on the course of this game."