The West Yorkshire club threatened to pull off an unlikely comeback, trailing just 22-16 with 11 minutes to go having been 16-0 down at the break.
However, Saints showed their killer touch at the death to deny Trinity what would have been a second win over the runaways Super League leaders this term.
“I’m really disappointed with those last two tries; they didn’t have to work at all to get them,” said Chester.
“It’s been a frustrating night.
“We build our game around high completions and making sure we kick the ball well.
“But after starting well in the first half we finished with six incomplete sets out of the last eight and kicked dead as well.
“That’s just asking for trouble against a side as good as Saints and we went 16-0 down in no time.
“We showed some effort and determination to get back into it but we have a lot to learn and we’ll be better for tonight.”
Chester did praise Bill Tupou, the in-form Aucklander centre who caused Saints all sorts of issues.
“There’s no better centre in the comp’ for me,” he said.
“You just have to look at his stats, the metres he’s made and when we’re in trouble we give the ball to Bill.
“He’s a very, very hard man to bring down. I’m certainly glad he’s in my team and deserves all the accolades he gets.”
Saints chief Justin Holbrook saw his side arrest their mini-slump after two successive losses.
And he was impressed by giant second-row Pauli Pauli whose try when Trinity were down to 12 men got the hosts back to 16-12.
“It was a barge over try but it’s almost illegal that,” said the Australian.
“He had half our team on him and still got the ball down!
“He could be next convert to NFL; get him out of our game – he’s too big!
“We knew how hard it’d be to come here and get a win so it was very pleasing to eventually get it.
“It was nip and tuck and a really good start to the game for both sides. There was not much in it so to come in leading 16-0 was fantastic.
“That was important to start well as the last couple of weeks we haven’t done that and made it hard for ourselves.
“We were concentrated, though, and ready to play and we managed that.”