Releasing a statement swiftly after Entwistle's departure was announced, Paxman has also predicted that the corporation's editorial problems are spread beyond Newsnight.
The BBC Two political review's practices have been brought into question following former editor Peter Rippon's decision to abandon a report into pedophilia claims surrounding Jimmy Savile, and a report last week which led to ex-Conservative Party treasurer Lord McAlpine being accused of child abuse on the internet.
Jeremy Paxman believes that the 2003 Hutton Inquiry, which strongly criticised the BBC for leaking quotations from Dr David Kelly, has increased the role of middle management at the expense of programme-making.
"George Entwistle's departure is a great shame. He has been brought low by cowards and incompetents," he said.
"The real problem here is the BBC's decision, in the wake of the Hutton Inquiry, to play safe by appointing biddable people."
"That is how you arrive at the current mess on Newsnight. I very much doubt the problem is unique to that programme."
Defending Entwistle's integrity, Paxman added: "I had hoped that George might stay to sort this out. It is a great pity that a talented man has been sacrificed."
The 62-year-old finally stated that "while time-servers prosper", he would "not be issuing any further statements or doing any interviews".
> Live: Reactions to George Entwistle resignation
> In full: George Entwistle's resignation statement
> Tim Davie to lead BBC as acting Director-General