Harry Cornick netted the only goal of the game as he converted from close range as he got on the end of James Collins' brilliant low cross, securing the Town's place in the third round draw.
Jones said: "It's a wonderful result, I thought it was a wonderful performance after the first 15 minutes where they came out of the traps. But once we stuck to the game-plan, I thought we were comfortable for most of the afternoon if I'm honest.
"You don't get to see us play like that very often where we sit back, be compact and then hit them on the counter attack as we know we have different facets, we know if we want to go to the next level, we're going to have to have that part of our game right at it and I thought we were excellent.
"For all the possession Bury had, we probably had the better chances and should have killed the game off earlier as we've had some wonderful chances on the counter attack. Realistically Sheasy's had one or two saves, they've missed their best chance in the first half where Danns missed and apart from that I thought it was a good cup tie, but I felt it was a reasonably comfortable afternoon."