Saidou Khan and George Carline scored the goals in each for the Spireites.
The Stones enjoyed some good possession at times and stayed in the game despite falling behind after five minutes but they failed to really test home stopper Scott Loach.
Craig Fasanmade, Joshua Umerah and Rhys Browne all had attempts at goal but they lacked a clinical edge.
"There are not going to be many teams that come to Chesterfield and dominate the game and I think we have dominated it,” Maynard said.
"When the second goal goes in it knocks the stuffing out of you and it is the game dead if I am being honest but up until that point we were the only team going to score and we just needed that little bit of quality.
"I thought we silenced their fans, after their first goal went in we had a 25-minute spell and then it just got to half-time. We probably needed another eight minutes before half-time, the fans were just starting to turn a little bit against them because we were dominating the game with the ball.
“I know we need a bit more end product, we have not worked their goalie enough but overall I am proud of the lads.”
He added: "If you go back six months as a football club we were coming here hoping not to lose three, four or five-nil.
"We have come here today and there was belief in the camp that we could actually get something.”