And the Wigan chairman believes the choice of the next Football Association chief is "crucial", believing Rick Parry to be "the perfect candidate".
Triesman stepped down as chairman of the FA and England's 2018 bid following allegations he accused the Spanish and Russian football federations of bribery.
The FA have yet to choose his replacement and Whelan insists the right candidate must be chosen - and soon.
He said: "I think Lord Triesman has been let down very, very badly but the damage is done. I think it's done an enormous amount of damage.
"Now the FA have got to appoint a new chairman as quickly as possible and when we appoint a new chairman we have to be very, very careful who we appoint because it will be crucial if we're going to get the World Cup.
"I know ex-politicians come into the reckoning but you've got to think about getting someone familiar who is into football big style, someone like Rick Parry.
"He was at Liverpool and was a brilliant chief executive. He's gone out of the game because I don't think he got in with the two owners at Liverpool - but he's a perfect candidate to take it on and lead them (the FA) forward.
"I'd much rather someone who's been at the sharp end of football. (Manchester United's) David Gill is a brilliant chief executive too. That type of man is the perfect candidate to lead the FA.
"I still hope and believe it (the World Cup) will come to us because we are the natural choice.
"I wouldn't give up hope on that - we can go forward and get it with a quality FA chairman."
Whelan believes currently the Premier League are best equipped to lead the game in this country.
He added on BBC Radio Five Live: "Wembley is the home of football in England. We've got to get it run properly and I think only the Premier League can run it properly.
"The FA are in debt to the tune of three-quarters of a billion pounds. Now we've got concerts and all kinds of things going on there to pay the interest charges on it.
"I don't mind other games at Wembley - rugby league has been there for years - but we shouldn't have pop concerts at the home of football.
"It needs a tough man in there, someone with the qualities to get hold of Wembley and shake it up.
"The FA have got to stop amateur people having too much say on how the professional side of the game is run.
"I'd like the Premier League to consider taking the FA stadium over and running the England team."