The visitors led at half-time through a Haydn Hollis own goal, and North End comfortably held on for the three points against a lacklustre Magpies side who are finding goals increasingly difficult to come by.
Grayson, who now has two wins and two draws to his name since taking over at Deepdale following the departure of Graham Westley, felt his side could have won by a bigger margin.
He said: "It's a good win to come here and build off the results we've had so far. We've kept a clean sheet and we could have scored four or five to be honest as we had some outstanding chances that we didn't take.
"We asked the players to show the same desire and attitude that they have done over the last few games and they've done that and I thought it was a really good performance.
"We mixed our game up well - we played when we could play and we battled and scrapped when we had to. There is a real desire among the players at the moment not to get beat."
However, Grayson added that despite the unbeaten run, his side would not be getting carried away.
"We are just looking to finish the season as positively as we can and take some momentum into next season," he said.
"We've come in and tried to give the players some belief as they are good players and I think they have underachieved. The players have been receptive to what we are trying to do."