The Owls manager has been the target of chants from supporters demanding he be sacked after a run of just one win in 10 games.
Wednesday kick-off the festive fixtures against Preston on Saturday, five points off the relegation zone, knowing they need a positive result before tough trips to Middlesbrough and West Brom.
Coach Bullen stepped in as caretaker boss on Christmas Eve last year, when Carlos Carvalhal left the club, and the former Owls player - who replaced Luhukay at today’s pre-match press conference - believes both managers have something in common.
"He (Jos) is a very strong character externally,” said Bullen.
"Carlos was the same and they are both tough characters in the way they handle the tough side of the game.
"He (Jos) comes in in a very positive mood.
"He's very much a fighter with regards to trying to sort things out.
"He's not one that is going to go about with his bottom lip out and head down.
"We have to stay positive and hopes that transmits to the field.”
Asked why Luhukay skipped Friday’s meeting with the media, Bullen replied: "We just thought we would mix it up.
“It has been a tough 10 weeks of results and everything. You try and look at how you can mix things up.
“We have obviously got a lot of preparation to do with regards to the Preston game.
“I have done it before with Carlos (Carvalhal) when results are going slightly different.
"It’s just a different face and different voice.”