Ollie Banks scored his fourth goal in three games and Armand Gnanduillet headed a second on the stroke of half time to boost Chesterfield's promotion challenge.
Tommy Lee marked his 200th League appearance for Chesterfield with a vital save to deny Billy Knott and celebrated a fourth consecutive clean sheet as Lynch reflected on a solid team display.
He said: "We didn't start the game well, we looked fearful and a little bit tired and if we had played like that in the second half I would have probably said 'bad day at the office, that's us' but to come out with that reaction and energy is very frustrating because I needed that in the first half.
"You are coming to a top team that is tipped for promotion and maybe the fear factor was there a little bit but to play the second half the way we did made me think why didn't we start the game like that.
"It's a double-edge sword, I was very encouraged by the second half when we changed the shape a bit but it shouldn't take a change of shape to get the energy levels going."
- Sports & Recreation