Lee Chung-Yong opened the scoring for the Trotters before Lukas Jutkiewicz's magnificent strike from long range in the 32nd minute saw them double their lead in the Sky Bet Championship tussle.
But Lewis Grabban was quick to respond, with an equally splendid strike, before Simon Francis headed in the second for the Cherries to secure a deserved point.
Freedman said: "I think there are long-term scars at the football club with certain players here and I think we need to try and shake them off and move on.
"We need stronger characters. It's a setback but it's not the end of the world.
"I picked a very attacking team and I thought in the first 35 minutes we were value for money and two-nil up.
"But when any setback comes our way it affects us big style and that's what happened today.
"In the second half Bournemouth were the better team and we rallied in the last 10 minutes and gave it a go. But I was disappointed because when you're two-nil up at home you should be holding onto that lead."
Freedman admitted that bringing players in would not be easy, though, with Bolton heavily in debt.
He added: "It's difficult right now and the board and I know exactly where we are right now. I wouldn't say there's a lack of funds but I wouldn't say that there are funds to go out there and improve us drastically.
"We've got to try and work with what we've got and maybe get one or two players in the loan market."
Bournemouth manager Eddie Howe believed that his side should have won the game.
Howe said: "I felt we deserved to win. I was disappointed that we didn't take all three points.
"It's mixed emotions for me because when you're two-nil down you're delighted to come back and get anything. But for the majority of the game I think we passed the ball better than Bolton, dominated possession and had more chances so it was a strange game."
"We felt that if we could get the first goal we'd have a really good chance of winning the game. Thankfully from going two goals down we responded really well."
Howe also suggested his team have grown as the season has gone on.
He said: "We took a couple of heavy beatings early on in the season and didn't respond well to chasing games.
"I think that we've learnt from that. I think we are a better side now and we showed good maturity today not to panic and try and chase the game early.
"We made good decisions with the ball and once we believed in how good we can be, then I think you saw a really good Bournemouth performance."