The search for a new team boss has begun and Wildcats have already received around 15 expressions of interest.
Smith quit on Tuesday, two days after Wildcats lost 42-28 at home to Catalans Dragons.
Speaking at a Wednesday press conference, chairman Michael Carter revealed he heard of Smith’s exit from another club.
Carter said Smith did not given an explanation, but the chairman revealed they had had a “frosty” relationship since Christmas.
“It was a bit of a strange one,”Carter said of Tuesday’s events.
“I had a text message from a ceo of another club asking if I was on the lookout for a new head coach, which came as a bit of a surprise.
“I texted him back saying I don’t know what you are on about, then within an hour - I guess - Brian walked into the office, said he was terminating his contract and walked out and that was it.”
Carter added: “I was a little stunned. He left the office straight away and I guess by the time I had come round he probably wasn’t still in the building.
“By his manner you could tell this wasn’t a decision that was going to get changed. He was terminating his contract and that was it.
“We have had a frosty relationship since Christmas for reasons that will stay with me. He was the highest-paid coach we have ever had [and] 19 of 31 squad members were signings or re-signings he sanctioned.
“It was the highest playing budget we’ve ever had and we’ve put extra resources into strength and conditioning, physio and training facilities at Featherstone.
“I’ve tried to back him to the hilt with everything he’s wanted, but I guess at the end of the day it was never enough.”
Smith took charge in June and guided them to victory over Bradford Bulls in last season’s million pound match, which kept them in Super League.
They have won one of their five league fixtures this year and travel to St Helens on Friday.
It has been a dramatic 24 hours, but Carter insisted: “Life goes on. This sort of thing is just part of life in professional sport.
“We have got to look forward, we have got a game at Saints on Friday night. Stu’s in charge of the team this week, I have spoken to [captain] Danny Kirmond and the lads are okay and looking forward to getting into battle with Saints.
“We will progress things as quickly as we can in terms of a new head coach.”
Meanwhile, former Leeds Rhinos and Castleford Tigers utility-player Jordan Tansey has left Wildcats to join Huddersfield Giants.