The Wanderers manager felt Kevin Davies was treated unfairly by ref Carl Berry, who also blew up for a Bolton free-kick when David Ngog was through on goal.
Freedman said: "Until referees at this level, which is a very important level, are full-time, I can't criticise the referee," said the Scot.
"The Premier League have got 18 full-time referees and that's the reason they're a lot better.
"Full-time is the way to go. They must be full-time trained, full-time fitness-wise and helped with things so they will understand the game more.
"I thought Kevin Davies was fantastic today but I just felt the referee didn't understand what he was doing. You can't blame him; you've got to blame the system.
"The poor guy has probably been asked to work all week to fend for his family and then he is asked to turn up in a stadium and make big decisions. It's unfair."
Davies scored Bolton's goal, which was cancelled out by Craig Davies, and Freedman said: "With the opportunities we created I felt that we deserved to win, but if you don't take your opportunities then it becomes very difficult.
"I'm disappointed in the nature of the Barnsley goal and the space he was given to shoot, but not in the performance or the number of chances we created."