The Australian, who took over in July 2016, lost his job on Tuesday. Even with just two wins from the opening seven games, the decision surprised many given that Stone secured a top-eight finish last term.
They have had injuries, too, with former England centre Cudjoe still yet to play this season following major knee surgery.
He said: “I was very disappointed on hearing the news. Rick’s a good bloke who worked extremely hard for the club as a whole.
“I got on well with him and was very surprised by the decision.
“I’m sure given time and getting some consistency with our team – and getting a few players back – we would have turned it around together, but that’s sport.
“As a squad, though, we should be ashamed as were very much a part of the reason for this decision. We’ve under-performed as a group and that’s something that we need to fix up quickly.”
Long-serving assistant coach Chris Thorman, 37, has taken over on a temporary basis and he takes charge for the first time when Huddersfield host champions Leeds Rhinos tomorrow.
Cudjoe, 29, said: “Chris is a very good coach and someone who I think could do a very good job.
“Depending on whether Chris has the job long or short-term will determine what he can bring to us as a group that’s different.
“But, either way, I think him alongside Andy Kelly and Luke Robinson will do a great job.
“Getting the right coach in is important but that’s not my job; as a squad we can’t worry about that. We just need to focus on getting back to playing well.”
Ahead of the derby with Leeds, who narrowly lost out to Castleford Tigers last week while Huddersfield were vanquished 48-10 at Wigan Warriors, Cudjoe added: “Leeds are a great side, the current champions so it’s going to be a tough game.
“We need to focus on ourselves and start having some pride and togetherness with our performances.”
Cudjoe, who was appointed captain by Stone in February last year, is making progress with his comeback.
“I’m going well,” he explained.
“I’ve started to get moving on some different surfaces and even done some running on grass which was a good feeling.
“There’s still no date on my return yet but I’m happy with where I’m at.”
Thorman, meanwhile, is grappling with an injury crisis as he prepares to take charge of his first match.
England winger Jermaine McGillvary is the Giants’ latest casualty as he faces a two-month lay-off with an ankle injury sustained in their 48-10 defeat at Wigan.
Ever-present stand-off Lee Gaskell is also ruled out of Friday’s game after being admitted to hospital with an infected elbow, the result of a collision with an advertising hoarding at the DW Stadium.
Gaskell, who remains in hospital, has been joined on the casualty list by second-row Dale Ferguson and centre Sam Wood, who were also injured against the Warriors.
Already without full-back Jake Mamo, Cudjoe, second-row Tom Symonds and prop Shannon Wakeman, Thorman has turned to products from his academy team for the clash with the reigning champions.
Darnell McIntosh, Tyler Dickinson, Jared Simpson and Sam Hewitt, an 18-year-old who only signed his first full-time contract earlier this month, are included in the 19-man squad.
Meanwhile, Leeds’ former Huddersfield vice-captain Brett Ferres is set to make his comeback against his old club.
The England second-row has been sidelined through knee surgery since October’s Grand Final but has been named in coach Brian McDermott’s 19-man squad.