And although Scotland confirmed suspicions that they will struggle once again this year after a 23-10 defeat by Wales, Woodward believes the Calcutta Cup clash at Murrayfield is still banana skin material.
"We're very self-critical at the best of times. We've been through a lot of aspects of the Italy game and I don't think we were operating at the world-class standards that we set for ourselves," he said.
"There was a lack of communication and continuity. We turned over the ball quite a few times. Also, the game was already won in the last 15 minutes but we weren't as ruthless as we could be.
"One or two players had fantastic games but then let themselves down in the last 10 minutes when they lost concentration a bit. So we've got heaps of work to do and I genuinely mean that.
"Scotland aren't as bad as people have made them out to be - Wales played very well on Saturday and obviously the match was away from home. Scotland had three new caps playing as well, so it was a brave selection.
"But Saturday is their big game and upsets do happen. We go there as favourites but we'll will have to be at our best to win the match."
Woodward's plea that the Scots are shown respect was echoed by his assistant coach Andy Robinson, who cited the Six Nations defeat by the Auld Enemy in 2000 as evidence of their ability to cause an upset.
That year England, hot favourites to land their first Grand Slam under Woodward, were edged 19-13 at Murrayfield in the last match of the tournament as Scotland adapted beautifully to the wet conditions.
The Six Nations title was still theirs, but that title had a hollow feel to it after the defeat in Edinburgh and Robinson is anxious to avoid more heartache on Saturday.
"Look what happened in 1999 - everyone said England just had to turn up to win and they lost," he said. "It's exactly the same on Saturday - we've got be at our best in these games to win them.
"Scotland have a lot of proud players in their side and they'll certainly bounce back this weekend."
England's work at the line-out was strong against Italy but Scotland should provide a more thorough examination of their pack with Scott Murray and Stuart Grimes proving accomplished operators.
"Our line-out functioned tremendously in Rome but the Scots have one of the best line-outs in the world," Robinson said.
"They get a lot of steals, so we have to respect them in that department. We've always enjoyed that battle.
"It sharpens your mind when you play against a side like Scotland because you know you have to be at your best in the line-out, otherwise they can really disrupt you."