Lynch said that the players executed the tactics perfectly and deserved the win for the effort that they put in, particularly in the first half.
"It was a game of two halves and Bury is always a tough place to come," Sky Sports News quotes him as saying.
"The lads conducted themselves superbly and they got the rewards for the hard work they put in during the first half.
"Full credit to the players because they dug in deep and gave a great account of themselves. It's a good pat on the back for the boys."
James O'Shea and Marc Richards scored the goals to give Chesterfield the win.