The two sides clash in the Premier League at Old Trafford on Wednesday.
"Big Sam went to Upton Park a year and a bit ago and the cynics said he's not a West Ham manager as he doesn't play football," Ferguson told the club's website.
"What was his mandate? To get them up into the Premier League as quickly as possible and he got them up within a year. Tell me someone else who could've done that."
Having had unhappy spells in charge of Newcastle United and Blackburn Rovers after eight years at Bolton Wanderers, Allardyce took West Ham straight back up to the Premier League from the Championship last term.
"He's also had to rebuild the team and get two or three players out because of their salaries," Ferguson added
"He's very underrated, it's as simple as that.
"There's a sort of impression about him being a certain type of manager. It's not really fair and I'm pleased he's back in the Premier League."
Paul Scholes is suspended for Wednesday's match while Ferguson has said fellow midfielder Anderson will start after an impressive cameo in the 3-1 win over Queens Park Rangers on Saturday.
Allardyce is hoping there will be no more controversial songs by West Ham fans at Old Trafford after condemning anti-Semitic chanting by supporters during Sunday's 3-1 defeat at Tottenham Hotspur.
A season-ticket holder has already been banned and the club are working with Spurs, who have strong Jewish ties, to identify others involved.
After the match Allardyce said he had not heard the chanting but told a news conference on Tuesday he was disappointed by what had been done "by a small minority of fans".
"Nobody condones that sort of behaviour and there is a zero tolerance attitude within the club," he said.
"I am sure Tottenham and the authorities will deal with it accordingly.
"Now I know what has gone on like everybody else I do not condone it or wish to hear any of that kind of chanting in football especially in this country."
West Ham's Mark Noble is suspended for the game while George McCartney will have a late fitness test.
