The West Yorkshire club looked set to take a giant step towards confirming a top-four spot when they led 16-12 heading into the final stages.
But Jonny Lomax capitalised on a glaring error from Scott Grix at the death as the Trinity full-back dawdled when preparing to deal with Mark Percival’s desperate kick ahead.
Wakefield had been the better side but Saints – who knew their season would be over if they lost – somehow salvaged the points.
Chester admitted: “I thought we were in total control for 78 minutes and lost to a lapse in concentration not just from Grixy but the middle guys not working hard enough on the inside and stopping offloads as well.
“He’s extremely disappointed – we all are – but the good thing about this group is we win together and lose together.
“No one will get it from me in the press or the video; we just couldn’t control their offloads in the last five minutes.
“Scott Grix has probably been my best signing this season. He’s a good kid. He will be hurting tonight but we need to put it to bed as soon as possible.”
Wakefield, who remain fourth, had also seen Liam Finn’s penalty strike an upright moments before Lomax’s try to add to the drama.
They had earlier dealt with being down to 12 men admirably while Dean Hadley was sin-binned.
Chester continued: “Myself and John (Kear) had a chat with six to seven minutes to go saying we looked comfortable.
“I’ll need to have a look at the video. Maybe we were too guilty of going into our shells a little early. We kept kicking (into touch) but continued to kick the ball out when Dean came back on the field, too.
“I need to have a look but I’m very proud of the efforts of one to 17. I’m a disappointed coach but pleased with that effort and we live to fight another day don’t we? It’s in our hands. We’ve two games left and we do it all again at Hull next Thursday and then Wigan here last.”
Meanwhile, St Helens prop Alex Walmsley left the ground after 65 minutes to rush to hospital as his partner went into labour with their first baby. However, the ex-Batley prop did not arrive in time to see the birth of his baby boy.