The Glovers started brightly in West Sussex but fell behind midway through the half to Ollie Palmer’s opener.
The visitors battled back to equalise through Carl Dickinson just before the break and looked to be the side in the ascendency before a disappointing second half.
Ashley Nathaniel-George restored the Reds’ lead before Filipe Morais added a third in stoppage time to inflict a first defeat on the road since the opening day of the season.
Still searching for a first win as a manager at the Checkatrade.com Stadium, Way was left frustrated with his side’s performance.
“We’re very disappointed,” he told iFollow Glovers. “There were periods where I thought we did well and there wasn’t much in the game until they took that 30-yard shot that flew in.
“The reaction after that was very poor and not like the way we’ve been playing. We’ve had more desire and more commitment to get the game back and I didn’t feel we showed that.
“We’re disappointed in the dressing room and the players have taken responsibility that they didn’t do well.”
Looking to claim a fourth consecutive win on the road, Town conceded their first goals away from home since the 1-0 defeat at Bury at the start of August.
Now without a win in three games against Crawley, Way is still searching for a 90-minute performance against the Reds.
“We’ve played here a number of times since I’ve been manager and we have not performed over a period of 90 minutes.
“You have to do that to win any football match. But I wanted the players to play 90 minutes like men and I felt that from our point of view, there were a few boys out there.
“I felt that there were good periods of play and we had large periods of possession certainly in the first half, but as I’ve said we never did enough to manage that game.”