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 today [Saturday] 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."
Jackett said he has no sympathy for Luton after the game, which is unsurprising given his connections to rivals Watford.
The Millwall boss is instead looking forward to the quarter-final draw and a return to npower Championship action on Tuesday.
"We look forward to the last eight - it is a big opportunity for us," said Jackett, whose fans let themselves down at one point in the second half by taunting home fans with "Taliban" chants.
"Of course we would like a big Premier League side at home. That would be the preference.
"We will take what comes tomorrow and then we will look forward very quickly to Tuesday night, when we play Peterborough at home.
"Hopefully we can take some confidence from today and get back on track in the league."
Luton's focus also returns to league action after a memorable cup run that began in October.
The 1959 runners-up have overcome Nuneaton, Dorchester, Wolves and Norwich on their run to the fifth round, leaving manager Paul Buckle proud.
"They always give their all this group of players," he said.
"Every player I have tried to sign has to have them qualities and they gave their all right to the very end.
"The biggest disappointment today was not scoring a goal because I really felt, with the chances we had, we deserved a minimum of one goal.
"The dream is over and it is disappointing because of the manner we've gone out, really.
"As professionals, we've gifted it to Millwall. We really have given them a leg up that they would have loved to have had.
"Kenny would have known bringing his team here was a difficult challenge.
"They were professional, cleared their lines and did the nasty side, but what we did never gave us a chance to them under pressure.
"But listen, it has been an unbelievable cup run. We've done great. I really thought we could get to the quarter-finals, but maybe next time."
For now, Buckle is just hoping to lead Luton back into the Football League.
"What we've got to do is get as happy and buzzing about the league as we have been in the cup," the Hatters boss said of his side, who currently sit outside the Conference Premier play-off spots.
"We have to understand that this great football club I am manager of is a non-league football club.
"As much as that hurts, that's the truth. To get out of this division, we've got to show some real fight, spirit and character and a lot of togetherness."