The Shaymen secured a first round tie with Morecambe after overcoming Warrington at the second attempt on Tuesday night.
But Fullarton isn't getting too carried away as immediately switches his focus to his side's upcoming league games.
“Obviously, I’m very pleased," Fullarton told the club's website. "Being a cup game, it’s about winning and getting through to the next round.
"Obviously, we had to take it to a replay and I think tonight the players showed quality and competency in everything that they did.
“But my thoughts are Eastleigh on Saturday. Cup games take care of themselves and we’ve got four or five games before the Morecambe FA Cup game so my focus is Eastleigh.
"Sorry not to indulge in the love of the cup but we are back in league action at home again and another chance for three points.”