After the departure of Craig Muir in the summer, the Falkirk Foundation went through a lengthy process to appoint his successor.
The club will compete in the newly-formed SWF League One, which replaces the SWF Championship regional divisions – which have been split into two separate leagues.
Speaking to the Herald, new boss Tully, who left Championship side Rossvale recently, says the club needs to realise its ambition.
“It kind of came out of the blue a wee bit, to be honest,” he explained. “I left Rossvale at the end of last season and they contacted me, asking if I was interested in coming to Falkirk.
"I took some time to go over it and I decided eventually it was the right move.
"My aim is to take the club to that next level and I wouldn’t be here unless I felt that was possible.
“With no disrespect to those previously at the club, when you consider the facilities here, the club has under-achieved over the past few years.
"I want the team to challenge at the top end of the table and, within my time in the women’s game, all of my sides have done that.”
Coming into the club late into the summer, Tully added he will need to build a new squad quickly, with a number of players already having moved on from the club before his arrival.
"A few faces have left the club already,” he said. “Some are off to college and university, which is fair enough, but it leaves a job to do for me and my team.
"I’ve only had a couple of sessions with the group already here and I want to bring in some new faces, for sure.
"The squad needs that, although I do feel there is already a good mix of experience and youth at the club and we have some real talent here that can make it at at a higher level if they work hard.
"I need to gauge who I can build the squad around and who maybe won’t see the game time they desire.”
With the Scottish Women’s Football restructure having taken place over the summer period, the league Falkirk will play is arguably weaker than last season’s Championship South.
Local rivals Stenhousemuir are among the Bairns opponents, while the likes of Edinburgh City and Airdrie will have their eyes on the title.
“Myself and the other members of the coaching staff have taken a keen focus on the league set-up,” Tully said.
“We have looked at the teams in our division and we believe getting into the Championship is a real possibility.
"Of course, it will be difficult but it is a real aim this season, I don’t want to be going for a mid-table finish.”
“It is familiar surroundings for me and I know the Falkirk area well from my time here as East Stirlingshire boss and when I played at Brockville back in the day.
"I still get a wee buzz being here at the stadium and the place can be a real asset for us and success is in the palm of hands here.”