Having already overcome Wolves and Norwich in this year's competition, the Blue Square Bet Premier club had their sights set on becoming the first non-league side to reach the last eight since 1914.
Millwall, though, had other ideas, with James Henry making the most of an early Janos Kovacs mistake to slot home the opener at Kenilworth Road.
On-loan Rob Hulse doubled Millwall's advantage with an exquisite hooked effort as half-time approached, before substitute Dany N'Guessan made it 3-0 by bundling home from close range.
"It was a very good win for us in a tough tie," Millwall manager Jackett said after leading the Lions to a first quarter-final appearance since 2004.
"They put is under a lot of pressure. Getting the first goal was a big thing in the game and it was an excellent opportunist goal from James Henry. We got our noses in front and it put us on the right track.
"We silenced them very early. They've got a very good home record over the last three months and before winning at Carrow Road, they beat Wolves here.
"They have had some giant-killing experience and it was a very professional job done by us and we're pleased to be through to the quarter-final of the FA Cup."