John Sheridan's men lost 2-1 at the Proact.
Chesterfield were unable to start their National League campaign with a win at the weekend.
The Spireites lost 2-1 to Dover at the Proact.
Scott Boden had put the hosts in front on seventy-two minutes with a coolly placed finished, but the lead only lasted five minutes.
Alfie Pavey levelled proceedings with a headed finish on seventy-seven minutes, before he went on to score the winner with five minutes remaining.
After the match, Chesterfield manager John Sheridan told Peak FM his players need to 'learn quickly';
"When we get the goal, we need to shut-up-shop and see the game through a lot better.
"I think it's because of the level we're at. We have people who're going to switch off.
"You have to have game management on the pitch and unfortunately we didn't see the match out in the way we should've done."
Sheridan's men return to action tomorrow night against Maidenhead.