The Lions are second bottom of the National League table but were boosted earlier this week by the news that Southwell had signed from Wycombe Wanderers.
The striker scored 54 times in two seasons for Boston United before his move into the Football League and Cox thinks he can rediscover that form at Nethermoor.
“I tried to sign him when he was at Boston and he went into the Football League at Wycombe,” Cox told the Yorkshire Evening Post.
“He is a player who can score all kinds of goals and is a natural goalscorer. I think we have signed an excellent addition when you look at the fine lines of our recent results.
“It is fine lines of three points or no points at the minute and we have got to do something about it, simple as.”
Cox is hoping to extend the loans of Nottingham Forest youngster Adam Crookes and Oxford United striker James Roberts. And he would also like to add more strength in depth to his Lions squad.
“We are working extremely hard,” he added. “Last week, we played a centre midfielder at centre-half in the middle of the back three due to a lack of bodies.
“We have had seven or eight sat on the treatment table and the frustration is that some of them have only featured a couple of times. But we cannot moan about it and must get on with it.”
For more news, reaction and action from across the National League, like us on Facebook and follow us on Twitter and Instagram.