Goals from Andy Crosby and Paul Hayes, his first since returning to Glanford Park in the summer, condemned Preston to leave North Lincolnshire pointless in midweek.
Their only victory has been over Sheffield Wednesday, who are the only side in the Football League still without a point to their name.
"It's getting a bit disheartening," Chilvers admitted to the Lancashire Evening Telegraph.
"It's annoying for us because everyone is working so hard as a team and as a squad. We are not getting the rub of the green, but we have got to keep going and hopefully we will turn results round.
"They say teams at the bottom end of the table don't get the luck and that's what has been happening with us.
"But I'm convinced that if we keep working hard then things will start to go our way."