Two first-half goals from Nathan Young-Coombes and Ethan Chislett secured the points for AFC Wimbledon.
The result leaves Crawley Town in the relegation zone of League Two with just one point from five games.
Tom Nichols spoke to reporters after the game, labeling the team’s performance ‘unacceptable’.
He said: “Today was not good enough. Unacceptable. First-half we were way off and the second goal before half-time kills any momentum.
"We lost out in most areas. We weren’t sharp enough with or without the ball. We didn’t win enough battles and we made sloppy mistakes.
"I include myself in this, we were not at it at all today. That’s not acceptable in any game – let alone a derby game.”
Some fans openly questioned Kevin Betsy’s leadership during the game as the club continues to look for their first League Two win of the season.
Chants of ‘we want Betsy out’ could be heard in the second-half and a chorus of boos erupted at the full-time whistle.
Tom added: "The fan’s are frustrated. We can hear that, we’re not stupid. We’re frustrated too.
"We know we’re not setting the right standards on the pitch. It’s not gone to plan. But it’s a process which is not going to come together overnight. The manager’s methods will be successful, it’s just taking a bit of time. Longer than we all want.
"It’s not pretty at the moment but we’ve got to work as hard as we can and get through it. It’s a tough period, but we all go through tough periods through our careers.
"We can’t give up now, we’re five games into the season. We’ve all just got to stick together and our luck will change."