This agonising defeat leaves Huddersfield Giants, third last season, at the bottom of the table going into the Middle-8s.
But new coach Rick Stone, who took over from axed Paul Anderson a fortnight ago, took heart from the performance.
Stone said: “We took some significant steps forward from last week.
“We just need to improve our concentration. We kept fighting, coming back and staying in the game. In a few weeks, I’d like to think we will show some reward for our work.
“We need to game manage things a bit better but that will come. Overall, everyone tried hard and our ball execution was positive.
“It looked like Warrington may run away at times but we stuck in there and kept ourselves in the fight.
“We need to get tougher defensively and the week off may be a good thing.”
Warrington coach and former Giants chief Tony Smith added: “Huddersfield are certainly not a bottom of the table team and they will be back soon.
“It’s a shame they are in the relegation area because they are a tough team to beat.”
Smith insists his side need to improve despite leapfrogging Wigan to finish second in the Super League regular season.
The struggling Giants led 30-28 until 20-year-old Wolves centre Toby King created the match-winning try for Daryl Clark four minutes from time.
The result saw Warrington finish runners-up to Hull but Smith, while impressed with some aspects of his side’s play, is demanding more from his players ahead of Saturday’s Challenge Cup semi-final against Wakefield.
He said: “It was entertainment on a large scale with action, suspense and joy for the home crowd at the end.
“There were some brilliant passages of play and some fantastic tries but we invited Huddersfield into the game at times when we seemed to have taken control.
“It was frustrating and we need to be better, certainly next week.”
Winger Gene Ormsby, who joined Huddersfield in a permanent deal a fortnight ago, bagged a hat-trick against his old club, with the visitors’ other tries coming from Aaron Murphy, Nathan Mason and Craig Huby.
For Warrington, Stefan Ratchford, Ben Currie, Ben Westwood, Chris Sandow and Ryan Atkins all touched down before Clark’s late decider.
Sandow was named the man of the match but Smith picked out Westwood for special praise.
He said: “Ben Westwood was outstanding and he was the best.
“Some of our attacking play was fantastic and it’s not all doom and gloom but we gifted our opponents the chance to score too many points.
Ratchford was forced out of the action midway through the first half in a daze but Smith said he would be fit to face Wakefield.
Warrington Wolves: Ratchford, Russell, T King, Atkins, Evans, Gidley, Sandow, Hill, Clark, Sims, Currie, Hughes, Westerman. Replacements: Dwyer, Westwood, Bailey, G. King.
Huddersfield Giants: Brierley, Murphy, Cudjoe, Connor, Ormsby, Brough, Ellis, Rapira, Hinchcliffe, Huby, Ta’ai, Lawrence, Ikahihifo. Replacements: Wood, Roberts, Mason, Crabtree.
Referee: J Smith.