George Entwistle's resignation was described as a "terrible mistake" on Saturday night by Labour's former culture secretary Ben Bradshaw.
He wrote on Twitter: "The departure of George Entwistle is a dreadful injustice and a terrible mistake. Who will sort the mess out now?"
Journalist and BBC Newsnight presenter Jeremy Paxman issued a statement on Saturday night saying: "George Entwistle's departure is a great shame. He has been brought low by cowards and incompetents.
"The real problem here is the BBC's decision, in the wake of the Hutton Inquiry, to play safe by appointing biddable people. They then compounded the problem by enforcing a series of cuts on programme budgets, while bloating the management. That is how you arrive at the current mess on Newsnight. I very much doubt the problem is unique to that programme.
"I had hoped that George might stay to sort this out. It is a great pity that a talented man has been sacrificed, while time-servers prosper.
"I shall not be issuing any further statements or doing any interviews."