The Bluebirds sit just above the relegation zone following yesterday's result - watch match highlights here.
Barrow's second manager of the season, Micky Moore, was sacked on Monday leaving Hornby to take charge in the interim.
He has explained what this week has been like: "Things happen in football and like I've said all week, desperately disappointed that Micky has left because he's a genuinely good guy but you've got to deal with things and circumstances as they are.
"I found out on Monday night, I spoke to Micky, he told me. It was just a case of going in Wednesday and preparing them and picking them up a little bit. To their credit, they've just got on with it as I would expect them.
"It's not a nice situation to be thrust into a job like this but that's football."
And on putting himself in the frame for the job, he said: "I've not thought about it. In all honesty, hand on heart, I haven't thought about anything like that."
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