James Lowry put Sheridan's side ahead from the penalty spot in the 21st minute, but goals from Danny Harrison, Adam Le Fondre and Kevin Ellison saw the Spireites slip to a second league defeat.
Sheridan said: "I thought for 65 minutes we looked very comfortable and had some great opportunities to kill the game off.
"If another one had gone in we would have gone on to win the game.
"We've got to learn how to win games, but it didn't happen, and in the last 25 minutes we gave away three very sloppy goals.
"Rotherham upped the tempo, but I knew they would come at us."