Freedman has been given little money by Bolton chiefs this summer and has so far spent only a minimal amount on Jermaine Beckford and Rob Hall, while also adding free agents Alex Baptiste and Marc Tierney to his squad.
Freedman said: "I believe we have made a couple of decent signings - we have not thrown money away.
"But there is room to grow. I think there is room for improvement. We are trying our best to do that."
Bolton have this week been struck by the news that Stuart Holden has suffered another serious knee injury, while Chung Yong Lee and David Ngog are still not fully fit, yet Freedman, who also worked under strict financial restrictions at Crystal Palace, is confident the Whites can once again challenge for a top-six spot in the Championship.
"I know what it takes, how to use a squad, when to be strong. Our results have not been great in pre-season, but you don't want to peak too soon," Freedman told the Daily Mirror.
Having helped nurture the likes of Wilfried Zaha and Jon Williams at Palace, Freedman is once again prepared to give chances to young players this season.
"I'm always excited about working with young players," the Scot added.
"Rob Hall is just 19, he has a long way to go, he has got to be a bit more mature every day in training. It's not a hobby, but a profession.
"I think he has got the talent, but he is only one year into senior football. He is a project, he will take time, but he is showing real signs.
"There's a lad called Sanmi Odelusi who I really love working with. I won't say what we pay him - it's embarrassing - but his enthusiasm is great."
Bolton open the Championship season with a trip to Burnley on Saturday, screened live by Sky Sports 1 (kick-off 12.15).