Second-half tries from centre Will Greenwood and replacement back-row forward Joe Worsley saw England home as they recorded a fourth successive victory over the Welsh.
But Wales, humbled by Italy in Rome last weekend, bounced back admirably in restricting England to a 26-9 win when the bookmakers had predicted a landslide loss.
"We had two objectives today - to win the game and not to concede a try," Woodward said.
"We achieved that, and everyone is pretty happy in the dressing room. The Welsh team must be applauded - it was a tremendous effort from them.
"From our point of view, it went according to plan, and hopefully, we will get a bit better every game and keep nudging forward."
Woodward saluted a towering performance from England number eight Lawrence Dallaglio, while also paying tribute to try-scoring centre Greenwood.
"Will was outstanding all-round. I thought he was brilliant, world class, while Lawrence also had a tremendous game.
"I'm sure that Wales can move on from here, and in no way was the game tougher than we expected.
"Wales are a good team - they showed a lot of passion, and I went into their dressing-room and told them that.
"We weren't surprised at all by Wales, although we lacked a bit of discipline which kept us on the back foot."
Woodward had no immediate post-match indication of England's injury problems, although clearly there are concerns about fly-half Jonny Wilkinson, full-back Jason Robinson and flanker Neil Back.
Greenwood admitted England were relieved to have kept their Grand Slam bid on course.
"They've taken a lot of flak, the Welsh boys and we are delighted to come away with a victory," Greenwood told BBC1.
"It's a difficult place to come and win at and it was one hell of a physical battle.
"This was a very proud Welsh team. They ran at us and disrupted us and it took all our concentration to win through."