The Giants appeared to be on course to end their campaign on a high after tries from brothers Louis and Innes Senior.
But David Mead scored four tries after half-time to inspire Catalans to back-to-back wins.
After Lambert Belmas, Mickael Simon and Ryan Hinchcliffe were all sin-binned by referee Greg Dolan in the second half, Australian Woolford expressed his frustration about officiating in Super League.
“I’ve said all along that there are a lot of good players over here, the adjudication of the sport over here is where the main differences are,” he said.
“The days of one referee are numbered and I think they are looking at a two-referee system next year. Things like offside and things that happen in the ruck will be more heavily scrutinised and it’s really hard for one referee to have a handle on.
“I thought both sides got away with being offside quite often and it was frustrating from our point of view.”
Despite ending the year with a fifth straight defeat, Woolford could not fault his side’s desire.
“At the start of the game we spoke about finishing with a really good effort and I thought our effort was outstanding,” he added.
“Over the past few weeks we’ve really struggled in attack with some key personnel being out but we had a couple of opportunities out there tonight – one before half-time and one just after and we weren’t able to land that killer blow.
“Credit to Catalans, when they got down our end they put on some points.
“I thought Josh Drinkwater’s kicking game was outstanding again and caught us out of position a couple of times.
“I’d say they were a little bit more composed and they took their opportunities whereas we were quite the opposite.”
Catalans Dragons: Albert, Mead, Jullien, Langi, Wiliame, Bird, Drinkwater, Simon, McIlorum, Moa, Casty, Goudemand, Baitieri. Substitutes: Anderson, Maria, Da Costa, Belmas.
Huddersfield Giants: Gaskell, McGillvary, L. Senior, Mamo, I. Senior, Russell, Brough, Clough, O’Brien, Matagi, Roberts, Mellor, Hinchcliffe. Substitutes: Leeming, Lawrence, Roche, English.
Referee: Gary Dolan (RFL).