Entwistle resigned Saturday after just 54 days on the job following a news report falsely accused a Conservative member of Parliament of sexually abusing a child, the BBC reported Monday.
Entwistle's contract entitled him to six months' pay but the payout represented a full year's salary. MPs described the amount as "over the top" and "outrageous."
Deputy Labor leader Harriet Harman said Entwistle should consider giving back half of the payment.
While stating the amount of the package was a matter for the BBC Trust, Culture Secretary Maria Miller charged the amount was "hard to justify" and "reward for failure" was inappropriate.
Christopher Patten, the head of the BBC Trust, said in a letter to Conservative MP John Whittingdale the amount was "justified and necessary."
Patten noted Entwistle would assist in two investigative reports related to hundreds of abuse allegations surrounding the late TV personality Jimmy Savile.
Entwistle has yet to respond to the MPs' comments.
The BBC director of news and her deputy have "stepped aside" pending an investigation into two bungled sex-abuse stories broadcast on "Newsnight," the BBC said.
The BBC said it fully expects Helen Boaden, director of news, and deputy Stephen Mitchell to be cleared of any wrongdoing.
The company said they merely "stepped aside" to remove themselves from decision-making while Nick Pollard, former head of rival Sky News, investigates the network.
The network said in a statement it wanted "to make it absolutely clear that neither Helen Boaden nor Stephen Mitchell had anything at all to do with the failed 'Newsnight' investigation into Lord [Alistair] McAlpine. Whilst recognizing this, the BBC also believes there is a lack of clarity in the lines of command and control in BBC News."