Danny Ings' deflected goal put Burnley ahead before Darren Pratley finished off a neat move before half-time to secure Bolton a point.
Freedman was satisfied with his team's performance against their local rivals and is keen to improve his squad further before the transfer window closes.
"You're always going to say you need one or two more players," Freedman told Sky Sports when asked if Bolton can challenge for automatic promotion.
"You've got to be careful with the amount of games you play in the Championship and, with one or two more players in with the right desire and hunger, we should be looking up a bit."
The Bolton boss added: "It's a well-earned point. It was a local derby and we had to make sure we had the grit and determination, and we certainly showed that.
"There were periods in the game where we showed our quality, especially in the first half, but we couldn't get the goal to get the lead.
"I thought maybe our crossing and finishing could have been better, we petered out a little bit, but our approach play and how we got in the pockets was good."