Substitute David Ngog scored a last-gasp equaliser after Alex Baptiste cut the deficit to one in the first half.
But Freedman felt that he recovered well and that his side could have snatched victory.
He said: "Once again we shot ourselves in the foot and gave them a 2-0 lead. We then showed great character and spirit and I believe that we did enough to eventually win the game in the end.
"Zat Knight will take it on the chin and after the mistakes there wasn't much else he did wrong in the game. He stood up and did well.
"But I'm not going to sit here and defend Zat because he's a big guy and he can do that himself. The fans are entitled to their opinion because they pay good money."
Freedman also accepted that he may have to sell players after the Trotters announced that they were more than £130million in debt, with Ngog heavily linked with a move away.
"Nobody's put a bid on the table for any of my players and David's a good young lad who's done well in training and took his chance today when he came on," he said.
"The club like every club have a policy and as the football manager I have to implement that policy.
"I have to make sure we're strong on the football field, but we've got financial fairplay in place so we have to cut our cloth accordingly."
Middlesbrough manager Aitor Karanka admitted his side did not deserve the three points, despite being moments away from victory.
The result ended a three-game winning streak for Boro and Karanka was not happy with his team.
"I think that today is the worse we have played since I came to the club," said Karanka
"I was disappointed that we could not hold on for the win, but I think that we didn't deserve to go 2-0 up and I'm sure that we can play much better than we did do today.
"We had five or six players who didn't play the last game, so I thought because of this my team could be a lot better than we were. I made the changes because I believe that they are the best 11 that I have at the club.
"But today we had no possession of the ball and we weren't comfortable on the pitch. We need to have the possession of the ball to keep them away from the counter-attacks.
"We played thinking that we were better than we are and we needed to play like we did in the previous three games."