Allardyce will not be the Hammers manager next season after his contract was not renewed, as announced on the club’s official website on Sunday.
The Englishman was appointed the West Ham boss in the summer of 2011 and guided them back to the Premier League.
Marsh seems to rate the 60-year-old highly, and has suggested that West Ham have made a mistake in not allowing him to carry on at the Boleyn Ground.
The 70-year-old has also highlighted the problems Newcastle United faced after Alan Pardew left for Crystal Palace at the start of this year.
Pardew was criticised by the Newcastle fans, who wanted him to play better football and were unhappy with his apparent lack of ambition.
Following the 53-year-old’s departure, the Magpies struggled for points under John Carver and narrowly avoid relegation from the Premier League.
Don't get why people are saying Big Sam is a failure. Good manager. #westham— Rodney Marsh (@RodneyMarsh10) May 25, 2015