They missed the chance to go back top of Super League following today’s 42-10 loss at John Smith’s Stadium.
They had been looking good leading 10-4 until captain Aidan Sezer was yellow-carded for a high tackle in the 34th minute.
Giants conceded four tries while the Australian scrum-half was off and never recovered, eventually conceding 38 unanswered points in their first defeat of the season.
“For that first half hour we were in the fight, 10-4 up and then Seze got put in the bin,” said Woolford.
“And we certainly didn’t handle that period well. They scored three tries in that six minutes before half-time and one straight after; to conede four tries in 10 minute period…
“We were a man down and it’s hard work but we needed to be better.
“The second half we were put under the pump by Wigan. We knew that was going to happen but I just don’t think we handled it well.
“I thought we got into some old habits and it was disappointing.
“Losing’s one thing but we’d conceded 26 points in three rounds - and then 42 today.
“You can’t blame that on having one guy in the bin for 10 minutes.
“We needed to show more resilience; they chanced their arm on that one at the end of the first half and fair play to them.
“But the other three we should have done better with. It’s that simple.
“We need to be a lot better as it’s probably not going to be the last time this year we’re down to 12 men. We need to learn from it.”
Woolford said he was “disappointed” with the yellow card for Sezer after his high tackle on Thomas Leuluai.
“But it’s what happens in this comp’; you can get a tackle wrong and the referees are quick to get the yellow card out,” he added.
“They saw something. It’s a tough call and it had a real influence on the game.
“Was it an intentional reckless tackle? I don’t think it was.
“Is it careless? It’s tough getting a yellow card for a careless tackle but they’re consistent with it, I’ll give the referees that.
“They’re quick to pull that yellow card out of their back pocket so it didn’t really surprise me.”
Woolford expects a response from his side who visit champions St Helens on Friday.
“We can’t kick stones,” he added.
“I said to the guys , the first three weeks certainly didn’t define our season and we can’t let this one loss define it either.
“We've got to make sure we dust ourselves down and get ready for our next challenge and learn from it.
“The good thing is we’ve got an easy game next week - against Saints!”
Meanwhile, Wigan boss Adrian Lam has backed Liam Marshall for England honours after the winger scored a hat-trick in that purple spell either side of the break.
One was a stunning chip and chase effort from his own 20, straight from a restart, to help Wigan move into first place.
On the uncapped 23-year-old, Lam said: "He was sensational.
"He can do some amazing things, and there's no doubt he's one of the best wingers in the competition right now.
"If he carries on like that, there's no reason why he can't feature for England later in the year.
"I was pleased for him, and I was pleased for the whole team. It was a good win.
"There was also the added bonus that we got a fair number of points on the board, which meant we've gone to the top of the league.
"I know it's still very early days, but we've got to be relatively pleased with the start we've made.
"The key now is obviously to keep building on it."