Forest's 3-1 win at Saltergate continued their unbeaten run under Barlow and Ian McParland and also saw them move within five points of a play-off place.
"I was pleased with the first half, the goals came at good times for us," Barlow told the club website.
"We were not as dominant in the second half. Chesterfield adjusted well to the conditions and were fired up.
"We played better later on but we were never comfortable until the third goal."