The Bluebirds relieved Micky Moore of his duties on Tuesday in the wake of the club's FA Cup exit at the hands of Evo-Stik League Shaw Lane on Sunday.
The team had won only once in the Vanarama National League - a home success over Boreham Wood - since Paul Cox stepped aside in August.
Assistant manager Neill Hornby will take charge of this weekend's league match at Ebbsfleet United.
But managing director Andrew Casson has hinted it may not be a short stay at the helm as Barrow weigh up their options to find the best way forward.
"It's not something that needs to be rushed," Casson said. "There is still a lot of football left to play, there are still a lot of points on the table.
"The next guy has to be the right guy to push us forward these next seven months, and be the right character, the right personality, to challenge this group of players, challenge us as a board, and make everyone get better.
"Barrow is always going to be a tough place to come and get points. You'd like to think that, even if you're not playing well, you'll still pick up quite a few points when teams come here. I don't think there is any great fear about losing ground."
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