The Labour peer and TV's Apprentice star made his comments yesterday as Government business spokesman Lord Popat said the banks who helped with the sale could receive up to £18.4 million in fees.
The Government has come under fire after the shares soared from the offer price of 330p when the majority of Royal Mail was sold off this month to at times more than £5.
Lord Sugar told the House of Lords that the Government had appointed the banks UBS, Lazards and Goldman Sachs for their "so called expertise in understanding the correct timing and pricing of the flotation of the Royal Mail".
He demanded from Lord Popat: "Why did these so called experts sell the stock at such low levels and get it totally wrong to such an extent that the stock rose by 33% the day afterwards and since then 54% on the issue price?
"Bearing in mind other reputable banks had come on record giving a valuation of £5 billion, why were these banks ignored and what will you be doing by way of an inquiry in finding out who the lucky institutions were that underwrote this bargain basement sale?"
Meanwhile, it has been confirmed that Business Secretary Vince Cable is to make a second appearance before the Commons Business Select Committee to be questioned over the privatisation, on November 20.
The committee has also written to investment bank Lazard, which advised on the sell-off, requesting that its representatives also appear.
It emerged yesterday that activist hedge fund The Children's Investment Fund Management (TCI) has amassed a 5.8% stake in Royal Mail.
It has bought 58.2 million shares, worth around £290m at today's 499p closing price.
Shadow trade minister Ian Murray said: "David Cameron's Royal Mail fire sale has seen the vast majority of shares going to big money investors in the City."