His injury-ravaged side almost pulled off an unlikely win against Warrington Wolves before eventually falling 19-18 at St Helens.
They saw four players suffer injuries during an absorbing contest including England Knights prop Matty English who was stretchered off after a shoulder charge by Ben Murdoch-Masila in the fourth minute.
There was clear contact to the head but the Tonga second-row was only sin-binned by referee Ben Thaler.
“I get confused over here about what’s yellow and red,” said Woolford.
“I’m still not across the rulings with the head high tackles. I’ve had this conversation with Steve Ganson before. You see love taps and accidental tackles that jump off the shoulders and clip blokes arond the chin and they get 10 minutes.
“I don’t think those types of tackles should be binned. They should be put on report. Tonight, though, while it was not intentional, it was a reckless tackle.
“We lost a player for the game - and it was three or four minutes in - and I guess it’s up to the match review panel now.
“But I’m not sure what constitutes a red and yellow over here with head shots.”
Woolford was full of praise for his side’s gutsy effort after they also lost second-row Ukuma Ta’ai in the first half, then Adam Walne as well as seeing captain and playmaker Aidan Sezer pull up in the final quarter after straining a hamstring while trying to convert Jermaine McGiullvary’s try.
“I think Warrington were entitled to win by 20 minutes,” he said, Huddersfield having also lost their first game back since lockdown by Golden Point at Leeds Rhinos.
“We lost two players in the first half and only had 13 men for the last 23 minutes.
“Seze was one of those and I think if he’d have been on we might still have got away with it given his experience and knowing how to game manage.
“But we just had every obstacle put in front of us.
“We put ourselves in a position to win the game, though, which was pleasing for me and after the adversity we saw against Leeds this was a giant step there tonight.
“We have to learn a few things and our young halves will learn a lot out of that but it was pleasing that we were right in there.”
Olly Russell, 20, came on for Sezer to score a try and convert to level the game at 18-18 in the 73rd minute.
But he failed to make the most of two drop-goal opportunities at the death as Giants’ chance went.
Woolford was delighted with the return of former England centre Leroy Cudjoe, though, who played the full 80 minutes in his first game in 14 months after a succession of knee injuries.
“I thought he was great,” he said.
“His work out of yardage was fantastic, defensively sound and confident with a couple of nice touches with the ball.
“He got into the clear with that chance and forgot what to do.
“I don’t think Jez (McGillvary) is a fast as he once was! He just expected Jez to be there.
“But it’s a big tick for Leroy.”
Thankfully, English was sat up and talking back in the dugout before half-time and Woolford expects him to be fine for their next game.