Allardyce said: "When you have lasted as long as Harry Redknapp has and started when he started and you are getting to your 60th birthday having just signed a three-and-a half-year deal, that says it all.
"He is, as a manager, one of the best in this country and has not been given the credit for it for one reason or another.
"It just shows that the man is extremely clever in how he goes about his job as a manager."
He continued: "He has spent a lot of money for a club like Portsmouth, but very wisely because of his international contacts.
"That is where I have come from over the last six or seven years, by building up the contacts internationally so the fear of buying a foreign player is perhaps less than other managers in the Premier League.
"That's where Harry has masterminded most of his managerial success, and he is, at the moment, doing very well that way.
"He has a fantastic backbone now and some very high energy, very skilful players who he has brought in from abroad."