Pope, the Valiants' leading scorer last season with 33 goals in all competitions, got off the mark for this campaign in the 3-1 league defeat to Wolves at the weekend and followed up that goal with two more against the Shakers on Tuesday night to give Adams' men a 2-1 victory in the Johnstone's Paint Trophy first round.
Adams said: "If Tom is being honest with himself, he's not the most confident player in a Vale shirt at the moment. He is having a tough time of it.
"He will have to look at his game, and we will. But he got himself a goal from a corner, which he is always capable of doing, and the second one was a great finish.
"But in his general play he's not firing on all cylinders and I think he still has a bit of work to do. Hopefully those two goals will help him."
Adams also paid tribute to goalkeeper Chris Neal who pulled off a string of second-half saves to frustrate Bury in an end-to-end contest.
Man-of-the-match Neal produced several fine saves, including two stunners to deny Shaun Harrad, before Pope won it for Vale in stoppage time.
"At times, we didn't defend well. If you don't do that then you need your keeper to come to the fore - and he was excellent," said Adams.
"Chris kept us in the game at 1-0 down and has obviously played a big part in getting us into the next round."