Scott Pollock struck a second half winner as the Pilgrims won for the first time since September.
And Culverhouse felt it was nothing more than his players had deserved.
“There is relief because we have not been at our best to say the least,” he said.
“I can't speak highly enough of the players, they played with passion, intensity and endeavour tonight.
“It was physical at times but the lads stood up to it and put a hell of a shift in.
“Alfreton asked a lot of questions because of how they play, they are well drilled.
“We had to stand up and be counted and the players were superb.
“I just thought we were superb, but that's the standard, we can't turn up one night and do that and then do what we did on Saturday.”