The Lions had few problems in seeing off the non-league battlers at Kenilworth Road with James Henry, Rob Hulse and Dany N'Guessan all getting on the scoresheet.
And with the prize of a last-eight spot, it was welcome relief from league duties with the London side currently in 12th, nine points from the play-off zone.
Jackett said: "We're very pleased to be in the quarter-final of the FA Cup, it's a great achievement. If we can get a home tie that would be fantastic.
"It's a fantastic opportunity to finish the season well. We want to get back on track in the Championship, we've lost our way, but performances like this will help.
"Scoring the first goal was key, if Luton got the first it would have been tough for us. It was a tough atmosphere today and we did the job very professionally."
Henry's opener in the 12th minute helped quieten the home fans and he added: "It settled all of us down and brought our fans into play, and we pushed on from there.
"They pushed us all the way, at 1-0 they had a good chance, but we just had that little bit of extra quality. It's a great result for us.
"We knew it was going to be a really difficult game and we're delighted to be in the last eight. We're one game away from Wembley now so we'll take anyone."