Berisha has endured a rare goal rut as the defending champion has fallen to second last on the ladder.
He's also been criticised by Australia international and ex-Roar captain Craig Moore for failing to make an impact.
The Albania international fluffed two clear-cut chances in the 1-0 loss to Perth Glory on Friday night and Brisbane desperately needs him to rediscover the spark and touch of last season when he scored a record 21 goals from 32 A-League matches.
While Berisha's hunger and work-rate remains high, Mulvey admitted his controversial marksman is suffering due to a lack of pressure from within.
"We need two players in every position pushing each other for that position," Mulvey said. "Besart doesn't have someone breathing down his neck saying `I'm ready to take your place'."
"If we can get competition for places it will keep everyone on their toes and we haven't quite got that."
"If you've got someone on your coat-tails who can play in your position it naturally gives you a bit of an edge."
Mulvey on Monday revealed he was looking "far and wide" to turn around Roar's fortunes during next month's transfer window, which opens on 1 January.
While Brisbane continues to dominate possession and create a host of chances, its lack of clinical finishing has cost it dearly.
"There's priorities across the board but we would like another striker," Mulvey said.
"Someone who would come in and add that little bit of quality to the squad.
"One thing I promised the Brisbane fans is that we're not going to die wondering. We're going to look for players."
Roar has room for one more player in its 23-man contracted squad but disgruntled defender Matt Jurman and midfielder Erik Paartalu are also reportedly keen for a transfer next month.
Brisbane will be without rising fullback Jack Hingert (hip) for four to six weeks, putting Jurman in line for a return to the bench away to second-placed Adelaide on Boxing Day.
The Reds are coming off a 6-1 thumping by Western Sydney.
"They'll be hurting a bit but you know what? We're hurting just as much," Mulvey said.