The ex-Notts County boss was appointed as Billy Heath’s successor last month and the Shaymen drew his first game in charge at Eastleigh.
They’re on the road again this Saturday when they travel to Woking, who have lost three of their last four.
Fullarton is keen to focus on his own side, however, and says his squad have quickly understood what their new boss wants from them.
He told the club’s website: “There is a willingness within the group to work on tactics that we have implemented into the squad. It is building the relationships as quickly as we can.
“The players understand the expectation and demand, and what they can expect from me.
“Every game we play; we will be looking to win. Every game is difficult in its own way and Saturday at Woking is an example of that.
“We can only control what we do in the game and how we impose ourselves on the game, that is the most important thing.”
For more news, reaction and action from across the National League, like us on Facebook and follow us on Twitter and Instagram.