Trinity led twice at Wigan Warriors and were ahead at half-time, but fell away in the final 40 minutes.
Reflecting on the 30-18 loss, Chester said: “I thought it was a really good contest and probably a tale of two halves.
“We didn’t want half-time to come, we finished the first half strongly.
“We had some decent field position and looked dangerous every time we got the ball, but we came out in the second half and gave too many penalties away.
“We only completed one set from our first five in the second half and you can’t afford to do that against Wigan.”
Trinity had won their opening four games, for the first time in Super League and Chester admitted: “The boys are disappointed, but it shows how far we’ve come as a playing group, that we’re disappointed we’ve come to Wigan and not got the result.
“I thought effort-wise we were brilliant from one to 17. Had we been a bit smarter in the second half things might have been different, but I’ve got no issues.
“I thought we were beaten by the better side overall, but I am proud of everybody.
“That has been our biggest challenge and unfortunately we just came up short against a better side.
“We wanted to go five from five, but we have started the season pretty strongly. We have to make sure this is just a little blip.”
Australian hooker Tyler Randell made his first appearance of the season after recovering from a knee injury and Chester feels he will add to the squad.
“His contact was really good and he looked sharp from dummy-half,” he said.
“He kicked the ball well and he will be better for that run.”
Warriors coach Shaun Wane was delighted with a fourth win from five attempts that lifts his side above Trinity into second place in the table, just two points behind arch rivals St Helens.
“It was a good win,” Wane said. “They’re a good, solid team, they were always going to be hard to beat.”