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The man renowned for his meticulous control-freakery during a spell in which he led England to their lone Rugby World Cup triumph, accused Lancaster and his staff of failing to plan properly.
"If you are coaching any team, the biggest thing is trying to be smart ahead of the game," he said following England's 20-14 loss.
"You have to be smart and a lot of that smartness comes from the way you train, the way you think and the players you pick."
Woodward, who last month resigned as the British Olympic Association's Director of Elite Performance, put the blame for the defeat squarely at England's decision to run their penalties, while Australia racked up points kicking theirs.
While there was an element of truth in captain Chris Robshaw's waspish riposte "hindsight is a wonderful thing", Woodward was adamant that, with better planning, England would have been better placed in the heat of battle.
"The key thing is getting these things in players' heads before they head out onto the pitch so you will know what will happen in every single situation," Woodward told the BBC.
"There is no point reviewing the video after you have lost, you have to review things before you go in and that is the secret to coaching.
"You must not make decisions in the heat of battle. It is a brutal business international rugby and these decisions are absolutely crucial.
"England have a week to put this right, and I think they will have a great week and it is a big opportunity for Stuart Lancaster to make his mark and turn this around."
England must now lift themselves for games against South Africa and New Zealand - two Tests in which anything other than 100 percent self-belief will prove fatal.
