He warned that staff involved in the programme shown last week could now face disciplinary action.
The BBC issued an unreserved apology on Friday night after one of the victims the programme spoke to admitted he had wrongly identified Lord McAlpine as the man who abused him in the 1970s and 1980s.
Steve Messham said he was “mortified” when he realised his mistake.
Mr Entwistle told the BBC Radio 4 Today programme: “We should not have put out a film that was so fundamentally wrong. What happened here is completely unacceptable.
“I have taken clear and decisive action to start to find out what happened and put things right.”
‘Further action will follow’
He said that he expected a report into what went wrong, being carried out by the director of BBC Scotland Ken MacQuarrie, to be on his desk by Sunday.
“Further action will follow from that – disciplinary if necessary.”
Mr Entwistle admitted the corporation was facing a “bad crisis” of trust in the wake of the Jimmy Savile scandal – including a decision to drop a Newsnight investigation exposing the late DJ as a serial child abuser.
Mr Entwistle insisted however that he had no intention of resigning, although he accepted that his future now lay in the hands of the BBC Trust.
“I am doing the right things to try and put this stuff straight. I am accountable to the Trust in that endeavour. If they do not feel I am doing the right things, then obviously I will be bound by their judgment,” he said.
Culture Secretary Maria Miller said: “I have been clear that the BBC Trust needs to get to the bottom, and quickly, of what has gone wrong at the corporation.
“The events of the last few days only serve to underline the vital importance of restoring credibility.
“I note that the BBC director general has commissioned an urgent investigation into these new Newsnight issues, and I hope that this work will be conducted and acted upon quickly.”