"I don’t understand the timing," he wrote in his column for the Daily Mail.
"Announcing that Eddie is to become the best-paid coach in history while other nations and clubs are on the verge of bankruptcy seemed insensitive, at best.
"That was a story that didn’t play out well in the current climate. There is going to be real hardship and rugby nations such as Fiji, Samoa and Tonga are struggling."
He also questioned the level of scrutiny that Jones has faced since England flopped in the 2019 World Cup final in Japan.
"Was there analysis at the RFU as to why they played so poorly in the final or why they went to Japan with only two scrum-halves and five props?" Woodward asked.
"Why was Joe Marler allowed to make a mockery of the press conference I attended in that final week? Who were the rugby celebrities coming and going from the camp and why did the team arrive at the stadium just 40 minutes before kick-off?"
LIST | 5 wonderkids who could star for England at 2023 Rugby World Cup
The England XV that started the 2019 Rugby World Cup final was the youngest ever to play in rugby union's showpiece, with every member of the starting side 30 years of age or younger.
However, head coach Eddie Jones - with his new deal locked in - believes a squad evolution will be necessary before France 2023, saying the current team 'doesn't have another World Cup in them'.
Here are five players who could potentially break into the England set-up...
One of England’s most exciting upcoming talents, the fullback is built in the same mould as All Black Damian Mckenzie. Safe under the high ball and blessed with incredible pace, expect him to play a key role f=or Newcastle Falcons on their return to the Premiership. Hopefully he'll then be in a place to make a bid for international honours.
Smith's rapid rise shows no signs of slowing down – it took barely a year for him to go from captaining Brighton College in an unbeaten season to involvement in the senior England squad. Therefore, it's not unthinkable that he'll be leading England's bid to lift the Webb Ellis Cup for a second time.
A lot of the English scrum-halves are ageing, meaning this is a direct choice between the Exeter Chiefs man and Ben Vellacott. However, his emergence as a premier playmaker in such a short space of time makes us think he will continue to get better, which will lead to him establishing himself in the England set-up.
The next star off the Saracens production line may be Kpoku, although the lock has been linked with a move to Northampton Saints due to the presence of Itoje, George Kruis and Nick Isiekwe at his current club. An incredibly hard-hitting carrier in the mould of Eben Etzebeth, a selection in the coming months would not be surprising.
A black belt in karate and also a former England schools finalist in gymnastics which would suggest the centre is blessed with power and poise! Has been involved in Eddie Jones's squad in the build-up to the 2019 Rugby World Cup and is someone we'd expect to step up heading into the 2021 Six Nations when he returns from Super Rugby and beyond.
Eddie Jones has signed a new contract as England head coach until 2023.
Who are some of the England youngsters that could feature at that World Cup?
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