Scotland beat England 20-17 at Murrayfield on Saturday (Sunday NZ time) after trailing 17-10 in the final quarter.
Woodward questioned six critical calls made by Jones, most notably his decision to replace starting flyhalf Marcus Smith after 63 minutes with England in the lead.
But the coach who guided England to the Rugby World Cup doubted there would be a "no-holds barred inquest" at England's Pennyhill Park training HQ.
"There is nobody at Twickenham qualified to hold Eddie Jones to account in the rugby sense, he clearly has them all in his pocket. He can’t be questioned, which is a massive weakness,'' Woodward wrote in his Mail on Sunday column.
"When he made a mess of the Six Nations last year the RFU apparently held a cosy little inquest with a collection of ‘rugby experts’, which was in itself an acknowledgement there was no one at Twickenham willing to question Jones."
Woodward suggested that England's leadership group question their coach's thinking "in the absence of anybody from above questioning Jones”.
"This is their team, they must take ownership. And those senior players should also admit to Eddie that they got things wrong as well. An adult conversation is badly needed."
“I think when he went off it must have been premeditated because he was going really well,’’ Matson said. “His opportunity to close out the game would have been great for him but it must have been premeditated.”