The reigning champions added the Giants to their list of scalps in 2021 and remain unbeaten.
Saints took a 12-0 lead into half-time and then added a third try before holding off the home team in the second half to claim the victory.
But Woolf believes his side can play much better and will do so as the campaign progresses.
He said: “I’m happy with how we’re travelling along.
“We’ve got a lot of improvement in us. What we’re doing is we’re all willing to work really hard.
“We know that we’re going to get better with the ball. I was a bit disappointed with the two tries we let in.
“We defended for long periods and then let in easy tries. That’s something we need to look at and improve.”
Woolf admitted it was a brutal contest and his men were fully tested by the Giants.
He added: “It certainly was very attritional.
“As we knew they would do Huddersfield came to play and they were desperate, and that made it hard.
“I was really happy with what we did in the first half. But we were quick to find things and made some errors off the back of that.
“In the second we had some really uncharacteristic errors at the start of the second half. But we were good enough to turn that around.
“All in all a good, tough win.”