Blake Austin claimed two tries, while Bryson Goodwin also grabbed two second-half tries with others coming from Ben Currie, Daryl Clark, Ben Murdoch-Masila and Chris Hill with Stefan Ratchford kicking nine goals.
Huddersfield claimed tries through Louis Senior, Darnell McIntosh and Alex Mellor while Oliver Russell landed three goals and a drop goal.
Woolford said “The worse thing that happened to us was half time. We played some good footy at the back end of the first half and got ourselves into a lead. The second half didn’t start great for us and went from bad to worse. There’s a lot of things where we need to be better at and there’s no excuses for getting 50 put on us. To go from 19-12 up at half time to 50-19 at full time is not acceptable.
“At the moment we’re not good enough to go with the top teams, it’s as simple as that.
“We spoke about looking for an 80-minute performance against a team like Warrington but we were way off in the second half.
“We lost a couple of players and had players busted but mentally I just think it gets too hard for us sometimes and we have got to turn that around as a team.”
Warrington coach Steve Price was delighted how his team responded in the second half.
Price said: “We actually played some reasonable football in the first half and it was just that 10 minutes prior to half time.
“We went error, error followed by penalty, penalty and the next minute we are 19-12 behind.
“We addressed a few things at half time and to come out and score 38 unanswered points in the second half it’s a credit to the players and showed the belief we have in each other,
Warrington: Ratchford, Lineham, Goodwin, King, Charnley, Austin, Patton, Hill, D. Clark, Cooper, Currie, Murdoch-Masila, Hughes. Substitutes: Tasi, Philbin, Akauola, Davis.
Huddersfield: McIntosh, McGillvary, L. Senior, I. Senior, Uate, Russell, Frawley, Clough, Leeming, Matagi, J. Wardle, Mellor, Lawrence. Substitutes: O’Brien, Murphy, English, Ta’ai.
Referee: T Grant (RFL).