Hatters duo Joaquin Gomez and Jared Roberts-Smith have both left the club to join former manager Nathan Jones at Stoke City.
Gomez, the club's first team coach, and Robert-Smith, who was head of sports scienceK, were both brought in by Jones when he took charge at Kenilworth Road.
Luton chief executive Gary Sweet admitted it was a blow to lose the pair after asking them to stay in the short term, but could understand their decision.
He said: "Nathan has taken Joaquin Gomez and Jared Roberts-Smith to Stoke City, who departed last night, which leaves us with a little bit of a gap, which has been filled this morning, as we have people to fill those spaces.
"Again, it was disappointing time-wise, I have to say. We asked them to give us more time with the two individuals who could have added quite bit of value to our upcoming fixtures, which was declined,
"They wanted to move on, which again, I sort of understand as once you make a decision in your own mind that you want make the next step in your career, then you want to do it as soon as possible.
"But here we are, we have the majority of the staff still in place and we've got some excellent young conditioning coaches and football coaches here that can step into those shoes temporarily until we find a manager who may well identify people to take steps into filling those spaces permanently."
Interim manager Mick Harford, who will be in the dug-out against Sunderland on Saturday, said: "It’s a shadow staff, as we lost three members of staff, Joaquin, Jared and of course Nathan.
"We lost three key members of the staff on match days and on a day-to-day basis, who were working really, really hard."
Meanwhile, speaking to the Potters' official website, Jones explained why he brought the pair in, adding: “To implement a club philosophy you need people you can trust and people who know how you work.
"You don’t need everybody who you have worked with because new people will buy into that.
"It was essential that my core staff came though.
"I don’t travel with a lot of baggage, I have a few who are essential, and the board were quick to say yes to those guys.”