Mitchell – who served a lengthy stint as Woodward's assistant in the England set-up before heading back to his homeland in 2000 – has recently come in for some heavy criticism from former All Black Christian Cullen in his new autobiography in which he describes Mitchell as a "dick" and said he did not trust him.
"I have to say it says more about Christian Cullen than it does about John Mitchell," Woodward told www.zurichpremiership.com.
"We know John Mitchell very well, he is an outstanding bloke and an outstanding coach, and you know from where I am sitting he has done a great job with the All Blacks, he has made them into a great team that everyone wants to watch. He has made some very, very tough decisions leaving out one or two big name players like Taine Randell, Cullen and Wilson.
"You will never hear a bad word about Mitchell from the England camp, he worked with us for a long time and never let us down, and there is stuff that he could have said but he didn't and that is why the guys like him so much and trust him so much. That's why I find the comments that come through just sad really, no more than that.
"As you can only pick 30 players for a World Cup and 15 for a game, I think that some players show their disappointment in ways that I don't think that is correct and I would be very, very disappointed if it happened in the England camp."
Meanwhile, Woodward has welcomed the decision to close the roof at the Docklands Stadium in Melbourne during Sunday's Pool C clash against Samoa.
With the city currently suffering from some unseasonal weather, England were forced to train in wet conditions earlier this week, but their coach is looking forward to 'perfect conditions' on match-day.
"I am just delighted that the roof is shut for Sunday night," he said.
"We know exactly what we are getting in terms of conditions, last time we played there we had a very good game against Australia and we have got a good ball handling side, so I am pleased that the conditions will be perfect on Sunday night. We have a tremendous pace in the team and incredible ball handling skill with the forwards.
"But there will be a lot of the players that played against South Africa playing at the weekend. I am looking forward to it and putting a lot of things right that we got wrong against South Africa with the ball in hand."