Wakefield scored a first-minute try through Ryan Hampshire but then conceded 30 unanswered points as the hosts kept in touch with leaders St Helens before their meeting next Friday night.
For Trinity it was their fifth straight Super League defeat and they are in danger of being dragged into the relegation dogfight as they continue to tumble down the table.
“We seem to be in panic mode a little bit and it’s been the story of the last five or six weeks,” said Chester.
“We were coming up with plays we’ve not really practised and kicking straight from a scrum with 20 minutes to go just shows where we are at at the minute.
“I questioned some of the guys last week whether they cared about each other but there was plenty of effort tonight which has been lacking over the last few weeks.
“So I was pleased with the response but obviously disappointed that we got beat.
“I thought we started the game really well with some real intent in our defence and got off to a really good start.
“I don’t think the half-time score (16-6) reflected the effort as they scored a couple of tries off kicks but we can take a lot from the first 40 minutes and take that into next week and give ourselves a chance of climbing up the table.”