Vale youngster James Lawrie had opened the scoring for Dean Glover's side with a 30-yard volley over a despairing Wayne Brown in the Bury goal.
Glover said: "The fans will always applaud effort and they could see the lads had given everything against a team who are gunning for promotion.
"We've got a very young side and it's a big learning curve for the boys.
People expect results straight away, but that isn't always possible and you need time.
"It was a great finish by James Lawrie and he will enjoy that. He's been champing at the bit for a start after scoring regularly for the reserves.
"His all round game was also good and he's walked away with the man of the match award. James is a clever player who pulls off defenders to create space. He's a fine prospect."