A late own goal from Shrewsbury right-back Ryan Woods sealed an eighth away victory of the season for the Deepdale club.
"The success that you can get is based at what you've got as a squad and what you can do to affect the game when it's not going your way," said Grayson.
"You look at our bench with Hume, Beavon, Holmes and Gallacher. They're all attack-minded players, who you can bring on at any time who are good enough to get into most League One teams if not Championship teams.
"We've got the bonus of doing that and we've got a good squad.
"There's a camaraderie about the group that when we win games we're all in it together. We've got good players who weren't even in the 18.
"We've got something going and long may it continue."
Grayson felt Preston's second-half display was an improvement on their earlier efforts as they were ran close at the Greenhous Meadow by struggling Shrewsbury.
He added: "We've said many times already this season you have to do whatever it takes to go and win a football match.
"First half we weren't good enough and we were second best when we had possession of the ball and when we didn't.
"We knew we had to up it quite a bit and we got back into the game and got a bit of pressure going.
"Then we've got the firepower to bring off the bench and try and change it round at any particular time and obviously that was a big factor."
- Sports & Recreation
- Paul Gallacher
- Lee Holmes