Jay O'Shea and Tendayi Darikwa were on target either side of half-time for the in-form Spireites before top scorer Tom Pope spearheaded a late Vale revival that ultimately fell flat.
"Credit to Chesterfield because they looked as though they wanted it more than us," he said.
"We didn't create anywhere near enough. We had opportunities to put the ball into the box in the first-half, but we kept having an extra touch and that let us down.
"Our front two were starved of decent service. The pitch cutting up badly didn't help, but it was the same for both sides and Chesterfield looked better than us.
"There were a few boos at the end, but we are having a decent season and we've got a big game at Cheltenham next Saturday when we will try to bounce back.
"When you lose games you can dig a hole and disappear, but we will dust ourselves down, work hard on the training ground and stick our heads above the parapet next weekend.
"Let's not forget that Chesterfield were one of the bookies favourites for promotion and they've got good players. They recently changed their manager and are on a decent run of form."
- Sports & Recreation