Lukas Jutkiewicz had put Wanderers ahead in the first half before Barnett appeared to be the last man when taking down Liam Trotter, who was through on goal.
But referee Darren Drysdale chose only to book Barnett, with substitute Nick Powell then going on to equalise late on before Jordi Gomez had a penalty saved by Adam Bogdan in injury time.
Freedman felt that the decision not to put Wigan down to 10 men changed the game.
Freedman said: "I don't like criticising referees and I thought he had a good match today but I was very, very disappointed by the decision he made.
"It was a decision which gave them that little bit of hope to get back in the game in the end.
"It's a difficult match for referees and I'm not one to criticise them because I know how difficult their job is, but I just can't get my head around the decision.
"He's through on goal and it's just a very poor decision. On the replay it's even worse.
"It's a huge turning point in the game and I think we had the opportunity to go 2-0 up. It's been a challenging time for us but these players put in a huge effort and we should be proud of that."
Despite the Trotters now only playing for pride, Freedman was also quick to dismiss that his players might drop their intensity.
He added: "That's not something that's going to happen at this football club. These players will not give up on anything. They will play for every minute."
Wigan manager Uwe Rosler was happy that his players managed to keep their impressive late-season run going with the draw.
However, he was not happy with his team's performance, and he said: "It was very important to get something out of today's game.
"Should I be happy? Should I be disappointed? I don't know.
"We had some experienced players put there who couldn't handle the derby situation and got nervous after they scored.
"Today we are disappointed in ourselves. We should have played a lot better from the start. As a ball playing team we should have been better on the ball and at times we didn't cope with the physical side of things.
"But at the end I only thought there was one team on the pitch.
"We have to play better (against Leicester) on Tuesday than we did today because we're playing the best team in the division."
Rosler also pleaded ignorance to the decision not to send Barnett off, adding: "As Arsene Wenger always says, I didn't see it.
"What I did see was an absolutely unnecessary free-kick given by the referee which allowed Bolton to break up field with their five strong players."