Oli Banks struck the opener with a rising effort in the 15th minute that beat Martin Rice from 18 yards even though the goalkeeper got a big hand to the strike.
Chesterfield surged further ahead four minutes later as Jay O'Shea beat Rice, who initially made a superb point-blank save, from close-range on the follow-up.
Rice denied O'Shea with another superb save at the start of the second half as Chesterfield again took the game to their struggling hosts.
"We had a frustrating result last week and we've had another one here, Knill said.
"I have to say that I thought we played reasonably well in the first half but we came in 2-0 down.
"It wasn't really about great goals by them but poor play by us but that has been the story of our season so far.
"For us to turn the situation around we have to be better than that.
"Goals change games. It changes everything doesn't it? The crowd are with you and all of a sudden you concede two quick goals and everything changes. Also you have to change, because you are now 2-0 down.
"We looked quite comfortable moving the ball around the pitch, then we concede two goals and your strategy changes doesn't it?
"Football changes quickly. It is only for us to change it again. We know that we are capable and a squad that is capable so we have to do it on the pitch, especially at home.
"The game at Accrington next Saturday is now a big game, a massive game. The good thing is that there are still plenty of games left but we have to do something pretty quickly."
- Sports & Recreation
- Martin Rice