The 61-year-old left his post with the national team on Wednesday by mutual consent, after agreeing with the Football Association that comments he made to The Daily Telegraph were “unacceptable”.
Allardyce was allegedly filmed by undercover journalists saying that he could offer guidance on how to circumvent FA laws on transfers, while also criticising England predecessor Roy Hodgson.
The former Sunderland boss stated that “entrapment had won”, though he conceded he had made an error with his remarks.
McClaren, who managed England from August 2006 to November 2007, believes Allardyce fell victim to the sort of investigation that could catch out any number of his contemporaries.
“I think it’s been a hugely disappointing couple of days for English football, and very, very sad for what’s happened to Sam Allardyce,” McClaren said at the Soccerex convention in Manchester. “It could happen to any of us in high-profile sports positions and Sam, innocently, has paid the price.
“It just shows you that at the level where sport is at, the elite, privacy can only be found within the four walls of your own home. Unfortunately a lot of managers are discovering that, other managers and profile people have been targeted as well.
“I just think we need closure on this and any information which newspapers or reporters glean … the FA should step in, or the information should be given to the FA and they make enquiries into the game or allegations, and if there is any wrongdoing that can be proved then that has to be cut out from our game.
“Personally I’m very sad and disappointed for Sam. Professionally, I think if there is info out there, the FA should deal with that and make enquiries because no-one wants to see a corrupt game.”