Leeds announced today they had signed the Halifax-born back-row on a three-year deal from 2020.
Mellor, 24, had firmly established himself at Huddersfield in the last three years since leaving Bradford Bulls and the West Yorkshire club was keen to keep him.
Woolford admitted: "Alex will be a loss, there's no doubt about that.
"Unfortunately there was a lot of tooing and froing in negotiations and I believe we made Alex a more than fair offer to what we value Alex at.
"It's part of footy and he's decided the best choice for his career moving forward is moving on.
"There'll be no hard feelings there from my point of view. Sometimes you lose players you don't really want to lose.
"All the best to him and we all move on."
In-form Mellor retains his place or Friday's game at Castleford Tigers as Woolford names and unchanged 19-man squad after their 55-2 win over Hull FC at Magic Weekend.
The Huddersfield coach expects the player to carry on as normal until the end of the season.
"Alex made it clear to me when he informed me that he was leaving that he was fully committed for this year and I'd expect nothing less," said Woolford.
"He's a good person. He's come a long way with his rugby league in the last 12 months and developed into a really good back-rower.
"He's a good person around the place, is popular and I wouldn't envisage there being any problems with Alex's attitude."
He added: "We'll replace Alex.
"We've already gone about that with the signing of Chester (Butler) from Halifax and we've got our eye on a couple of others as well.
"There'll certainly be a hole there but we'll well and truly fill that before pre-season."
Woolford is not expecting major overhauls in their 2020 squad.
"Not really; we don't have many off contract so our hands are tied a bit," he said.
"It might be a little different next year as we have a lot off contract then.
"We've signed one new one (Butler) and I imagine there'll be another couple."
Meanwhile, the Australian added that captain Leroy Cudjoe - the former England centre who on his way back from knee surgery - is fit for selection for the first time this year but will be given another week's training before coming into his squad.