The 38-year-old has been severely hampered by back problems in 2014 and released a statement on Wednesday confirming that he will not be available to feature at Gleneagles next month.
Despite winning 14 majors - a tally bettered only by Jack Nicklaus - and being the dominant force in strokeplay golf over the past 20 years, Woods has often struggled to make his mark on the Ryder Cup.
The United States' only victory in the last six editions of the biennial event came at Valhalla in 2008 when Woods was recovering from knee surgery.
However, Woods does boast an impressive singles record and Huggett, who captained Great Britain and Ireland's team in 1977 following six appearances as a player, expects the USA to miss their most high-profile player.
"I do think Tiger is a loss, because even an 80 per cent Tiger would be a plus for the team," Huggett told Perform.
"I think Tiger over the years has done pretty well in the Ryder Cup; he's only lost one singles match anyway.
"It's not just on the course - Tiger is more of a team man than people might give him credit for.
"I would love to have Tiger on my team. I think just him actual sitting in the locker room, if you like, that would be enough to give you a bit of a spur."
Huggett praised Woods for sparing US captain Tom Watson a difficult decision when it comes to choosing his wildcards.
"I think it would have been the right thing for Tom to do to pick him," added the 77-year-old.
"But Tiger pulling out is the right decision and he's done a good job there because he's saved Tom a lot of worry.
"Tiger has actually made his [Watson's] mind up for him and I think you've got to applaud Tiger for that."
Woods is not the only American player to have suffered injury trouble in the lead-up to the Ryder Cup, which will be played in Scotland from September 26-28.
Matt Kuchar - one of the automatic qualifiers for the US side - and Jason Dufner, a likely wildcard selection, each withdrew from last week's US PGA Championship with respective back and neck problems.
And Huggett cannot see past a European triumph at Gleneagles.
"Personally, I think it looks very one-sided to Europe on paper," he said. "I can see Europe winning reasonably easily myself - and I never thought I'd ever be saying that.
"This year, not only has Tiger dropped out, two of the other players [Kuchar and Dufner] have got big question marks over whether they are going to play at Gleneagles. So I think overall they are going to have a very inexperienced team."
Having talked down America's chances of success, Huggett joked: "My house is for sale at the moment and I'm actually thinking of putting my house on Europe."