Time Loughton, the Conservative former children's minister, told the BBC Radio 4 Today programme that Sharon Shoesmith's payout was "effectively rewarding failure".
Conservative MP Charlotte Leslie, a member of the Commons education select committee said, Sharon Shoesmith should "demonstrate personal responsibility" following the Baby P tragedy.
The MP told Newsnight, "A blame culture is not the same as a culture in which people take responsibility and accountability."
Ms Shoesmith's lawyers argued that she was the victim of ''a flagrant breach of natural justice'' fuelled by a media witch-hunt.
Former child protection boss Sharon Shoesmith is set to receive a six-figure payout for being unfairly dismissed following the Baby P tragedy, according to BBC 2's Newsnight.
A settlement which could reach up to £600,000 has been agreed, although Ms Shoesmith may receive a lower sum, the programme reported, stating that some of the money will come from central Government.
Ed Balls, while Education Secretary, removed Ms Shoesmith from her £133,000-a-year post as Haringey Council's director of children's services after a damning report on the death of Peter Connolly, known as Baby P.
She was then fired by the north London council without compensation in December 2008, after a report from regulator Ofsted exposed how her department had failed to protect 17-month-old boy.
The Parole Board deciding whether Baby P's mother Tracey Connelly should be released was not looking at what happened to Baby Peter himself - they don't consider how serious that crime was.
What they are purely looking at is whether she still poses any kind of risk to the public and they have obviously decided that she doesn't.
Justice Secretary Chris Grayling will now take the final decision of how and when it will happen and Connelly will remain on licence, so if she steps out of order she will be sent back to prison.
The Ministry of Justice said Baby P's mother Tracey Connelly will be subject to strict controls and restrictions following her release from prison for as long as is required.
A Ministry of Justice spokeswoman said:
Baby P's mother Tracey Connelly was given a so-called imprisonment for public protection (IPP) sentence, which carries a minimum term.
An IPP sentence prisoner is eligible to be considered for release by the Parole Board when the minimum term is served.
When making its decision, the Parole Board will take into account the nature of the offence, the prisoner's offending history, the prisoner's progress in prison and any statements made on behalf of the victim.
Reports from psychologists, probation officers and prison officers are also taken into account.
Connelly will remain on licence for the rest of her life and if she breaches any of the conditions, she will likely be recalled to custody.
Peter Connelly, known as Baby P, had more than 50 injuries across his body when he died on 3 August 2007.
Baby P was on the at-risk register and received 60 visits from social workers, police and health professionals over a period of eight months.
His mother Tracey Connelly, her boyfriend Steven Barker and his brother Jason Owen were all jailed for causing or allowing the death of Peter.
In May 2009, Tracey Connelly was given a so-called imprisonment for public protection (IPP) sentence and was jailed indefinitely with a minimum of five years.
A statement from the Parole Board has said that Secretary of State will make arrangements for the release of the mother of Baby P in due course.
The mother of Baby P Tracey Connelly is to be released from prison, the Parole Board has confirmed. Connelly was jailed indefinitely with a minimum of five years in May 2009 for causing or allowing her son Peter's death.
The Parole Board has recommended her release from prison following a second review of her case.
The Parole Board said today it has directed the release of the mother of Baby P, Tracey Connelly, who was jailed indefinitely with a minimum of five years in May 2009 for causing or allowing her son's death.