While Cleary was proud of the way his players dealt with the saga, the Raiders stumbled out of the blocks in front of 14,583 fans and they now can no longer make the top eight.
Wests on the other hand have kept their NRL finals hopes alive, drawing within two points of the eighth-placed Brisbane Broncos with three rounds remaining.
It also kept Benji Marshall and Robbie Farah's unbeaten run against the Raiders going when they've played together.
Things started to go wrong for the Raiders before the game began with half Aidan Sezer (hamstring) ruled out, forcing Elliott Whitehead into the centres.
Centre Joey Leilua's sin binning for a professional foul after just 10 minutes only compounded things.
When Wests had run in three tries in the space of seven minutes it turned out to be the final nail in the Green Machine's season.
Wests winger Malakai Watene-Zelezniak, Moses Mbye and Michael Chee-Kam all crossed to make it 16-0 before Leilua returned to the field to even the numbers again.
"It killed us. They scored three tries, it was 16-0 when Joey came back onto the field. For us to hang in there and get back into the game I thought it was a real big effort," Raiders coach Ricky Stuart said about the start.
"It was never in doubt with these boys, I know I'm going to get the effort every week no matter what the situation. It doesn't subtract from any of the disappointment."
Chee-Kam had a big day with 145 run metres on top of his try.
The first of Joe Tapine's two tries and then Josh Papalii's four-pointer, on either side of David Nofoaluma scoring, pulled the Raiders back into the contest to trail 20-10 at half-time.
Wests flew out of the sheds and looked like they could run away with the game with hooker Robbie Farah looking dangerous around the ruck.
But they only managed a penalty goal before the game into a grind, off the back of Jordan Rapana and Papalii's tireless work.
Second-phase play led to Leilua's try and then Tapine crossed for his second to make it a two-point game with 15 minutes left.
Stuart said Tapine was an important part of the Raiders' future.
He ran for 156m and looked dangerous every time he got the ball.
"They doubled up on him in defence and he still created havoc. He's a wonderful talent and he will be part of our team for the future," Stuart said.
But a few errors, penalties and poor decisions halted their momentum.
Sezer is a "wait and see" prospect to face the ladder-leading Sydney Roosters at Canberra Stadium on Saturday.
WESTS TIGERS 22 (Malakai Watene-Zelezniak, Moses Mbye, Michael Chee-Kam, David Noafaluma tries; Esan Marsters 3 goals) bt CANBERRA RAIDERS 20 (Joe Tapine 2, Josh Papalii, Joey Leilua tries; Sam Williams 2 goals) at Canberra Stadium. Referees: Ben Cummins, Chris Butler. Crowd: 14,583.