Trinity were beaten 25-22, after trailing 18-0 inside half an hour.
It was Wakefield’s second successive defeat by Giants, following their Ladbrokes Challenge Cup exit and after winning their opening four Betfred Super League fixtures, they have lost eight of their last 10.
“It took us 30 minutes to get into the game,” Chester admitted.
“There was some poor discipline from us, a couple of errors and yardage penalties.
“We just didn’t help ourselves in that first half.
“I thought from the 30th minute to the 80th we were the better side, but you can’t afford to give 18 points away and that’s what we did in that first 30 minutes.
“That’s what hurt us.”
Despite Trinity’s fightback, Chester stressed he couldn’t argue with the result.
“I don’t think we deserved anything from the game, because of the start we had,” he conceded.
“Our kicking game wasn’t great and we didn’t do the tough stuff in the first 30 minutes.
“We probably got out-enthused by a really energetic, young Huddersfield team.
“We need to have a look at the reasons why.
“We came up with a bit of fight towards the end, but the very last play of the game typifies us – we missed touch with a penalty.
“We are just not clicking at the minute, but credit to Huddersfield, they dug in.
“We had some opportunities to win the game but the final pass, or a knock-on, let us down.”
Chester insisted he remains confident Trinity will finish in the top-eight.
“Once we start clicking we know we are a good side,” he said.
“We are just not getting an even share of possession. The first 30 minutes was probably the worst I have seen us play.”
Trinity were without Anthony England who was ill.
He is expected to return for Friday’s game at Widnes Vikings, but Craig Huby is in doubt due to a knee injury.