Chester was relieved of his duties on Tuesday, less than 48 hours after a 22-18 loss at Huddersfield Giants signaled a fifth straight loss for the West Yorkshire club.
But loose forward Westerman, 31, told The Yorkshire Post: “I didn’t see it coming.
“I am gutted. After the last 18 months we’ve had with Covid, no fans in grounds, players dropping out and us playing games when we should have called them off, I do think it’s a tough one.
“I have found it difficult as Chez wasn’t just my coach but a good mate, too.
“I owe him a lot as he has helped me get my love for the game back and he’s helped me get back into the England squad as well.
“There’s a lot you have to look at but, personally, I don’t think it was the right thing to do.
“I do, though, understand why (CEO) Michael (Carter), (chairman) John (Minards) and the board came up with the decision.
“It’s tough. There’s the fans as well - I think they wanted this - but it’s not the way I thought it would go.”
Westerman, who rejoins Castleford Tigers at the end of the season, bellieves Sunday’s loss - when Trinity squandered an 18-0 lead - will have been a major factor.
“As players, we have to take some responsibility,” he added.
“To be 18 nil up like that, and end up losing from that position, that’s just down to the players.
“In the weeks before, when we’ve been losing, we’ve had too many individuals just not at their best.
“When you have four or five like that and you lose, do you get rid of the four or five or the one (coach)?”
Assistant Willie Poching has taken over as interim head coach and, with just four wins from 17 games, it is obvious what Trinity need to do starting when they host Warrington Wolves on Sunday.
“It’s always tough in these situations but we’ve been in today,” added Westerman.
“Willie and Andy Last are in there and they’ll be taking over.
“We just need to try and get to the end of the season and get a couple of wins under our belt.”