Allardyce's men have enjoyed a confident start to life in the top flight, currently sitting eighth in the table after picking up 19 points from 13 matches.
And Ferguson expressed his delight that the former Newcastle United and Blackburn Rovers boss has managed to prove the doubters wrong.
"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 official 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?
"He's also had to rebuild the team and get two or three players out because of their salaries.
"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.
"The Blackburn situation was one of the craziest things I've ever seen but I think Sam was more disappointed with what happened at Newcastle. He was unlucky that a new owner came in and wanted a certain type.
"He didn't get a chance in his first really big job with the expectation and fan base up there - he didn't get a chance to do the job right."