Fullarton left his role as the Saddlers’ technical director last month after just a year at the club.
The 46-year-old had overseen the appointment of two bosses in Matt Taylor and Michael Flynn, as well as two transfer windows.
Addressing Fullarton’s exit during a sit-down interview with the Express & Star, Pomlett said he and the Scot both agreed his tenure ‘had run its course’.
“Michael’s a very different animal than Matt. Matt was new into League Two football, and Michael isn’t. So, the whole dynamic of the club is different,” said Pomlett.
“The support around Matthew is different than Michael.
“Having said that, I still think a technical director is the right appointment.
“In time, that’s what I will revisit. I’m not in the process of revisiting it at the moment, but I’ll revisit it.
“With Jamie, it had run its course. He found Matthew to the remit I gave him and found Michael to the remit I gave him.
“But it had run its course. He felt it. I felt it.
“We needed to change, and so we were sat in the room and amicably made the change.
“It doesn’t mean I’ve thrown away the template of having a sporting/technical director.
“But at the moment, with how Michael operates with Wayne (Hatswell, assistant boss), let’s let that run for the time being.
“It’s an attractive model (having a technical director), particularly for a chairman.
“You have someone on the board looking after footballing matters for the club and the academy, so there’s a lot to be said about the role.
“But at the moment, I’m concentrated on making sure Michael is getting the support he needs to build a squad capable of challenging next year.”
Fullarton’s first managerial appointment was Taylor, who was sacked in February following a seven-game losing run.
The overhaul of the squad last summer led by Fullarton did not prove to be a resounding success, with work in the January window also providing mixed results as the Saddlers ultimately finished 16h in League Two.
Flynn, who has impressed since taking charge, is now overseeing recruitment.
One feature Pomlett says Walsall should benefit from is loans from nearby Premier League clubs.
“I particularly want us to have better relationships,” said Pomlett.
“We’ve had good relationships, and the one with Villa has been good as their ladies play here.
“But I would expect us to have a couple of local Premier League players here at Walsall moving forward.
“We’re working on that at the moment, so I’d expect that to be the case.
“You’ve got to be careful as they don’t always work. It’s a much different environment.
“Tyrese Shade came in from Leicester and found his feet, but it’s a hell of a baptism.
“If you get it right, like with Carl Rushworth, it can be fantastic.
“I still think we should be better at it than we have been (having those relationships with nearby clubs), and I expect that to happen.”