The Sheffield Wednesday manager is under mounting pressure.
Having struggled with injuries over the past two campaigns, the Owls were dealt another blow this week with the news that Fernando Forestieri will miss the next six-eight weeks with a hamstring problem.
But speaking to BBC Radio Sheffield on Friday, Luhukay insisted that Wednesday's issues cannot be blamed on either he or his medical staff.
"We have players who are in the situation that, in the whole season, not one time, often two, three or four times, maybe have injuries. This is a problem for this team and we must handle that," he explained.
"This has nothing to do with our medical team. This is to do with players who in this league, they have problems with high intensity, every game new, from the physical side.
"That is not new in this season, it was also a problem last season. Give me five players who played more than 25 games.
"This is the reality, that we have not enough players who can play more than 25 games in the Championship."
But asked if the root cause is therefore bad recruitment, Luhukay - who has been granted only three signings in 11 months - replied: "I cannot now say how the situation was when i came. I look only to the situation as it now is."
In terms of outfield players, only Adam Reach (45), Tom Lees, Barry Bannan, the now departed Jack Hunt (all 28), and Morgan Fox (26) started more than 25 of Sheffield Wednesday's 2017-18 league games.
And three of those - Reach, Lees and Bannan (all 19) - are already well on course to matching that this time around, alongside Joey Pelupessy (18).
Sheffield Wednesday fans - How alarmed are you by Luhukay's comments? Is he right?