Luhukay has come under increasing pressure following a run of just one victory in nine Championship matches which has seen the Owls slide from sixth to 17th in the table.
Wednesdayites turned on Luhukay following Saturday's 2-2 draw with lowly Rotherham United, chanting 'we want Jos out' and '˜you're getting sacked in the morning' in the second half.
Luhukay, who has signed just three players since taking on the Owls reins last January, took charge of training yesterday and looks set to be in charge for the trip to Swansea City this weekend.
Reach told The Star: "I think it (criticism of Luhukay) is unfair. We are all under-performing as players. That's not the manager's fault that we are not giving performances like we have done in the last couple of years since I have been here.
"At the end of the day, it's not about tactics or formations, it's about working harder than the other team, winning your headers and tackles. We didn't do that against Blackburn. We did it better (against Rotherham) but still not good enough."
Wednesday face Swansea, Preston North End, Middlesbrough and West Bromwich Albion before the end of the year as Luhukay's troops look to put some distance between themselves and the bottom three.
"It's vital we get some results (over Christmas), playing three games in six or seven days," said Reach. "You can quickly pick points up.
"But firstly we have to concentrate on Swansea on Saturday, because they are in the top end of the table. We need to look to teams like that to start clawing some points back.
"It will be very difficult. They are only recently went down from the Premier League, they have changed their philosophyand a lot of players from last season, but are coming into some good form.
"Their confidence is high and they will look at Sheffield Wednesday and think '˜their confidence is low, so it's going to be an easy game'.
"But it will be far from that, because we will rally together this week and work hard in training."
Wednesday's FA Cup third round meeting with Luton Town will take place at Hillsborough on Saturday, January 5. The tie has been selected for overseas live broadcast and will kick off at 12.30pm.