Brines was in charge of the Hoops' 1-0 win over Aberdeen at Parkhead on Saturday, a victory which lifted Gordon Strachan's side back to the top of the SPL.
However, the match official caused controversy in the dying moments of the game when he ruled out a late leveller from the Dons' Zander Diamond.
Brines penalised Diamond for handball, but television replays have shown that the defender clearly won the ball with his head in the build up to his late strike.
"From the angle I had adopted, I observed the Aberdeen player Diamond jump to meet the ball and I believed he used his hand to aid the ball's flight beyond him," the referee explained on the SFA's website.
"Immediately I blew my whistle awarding a free-kick to Celtic.
"The majority of players reacted to the whistle by stopping, the exception being Diamond who placed the ball into the Celtic goal.
"On reflection and having had the opportunity to view the incident via television, I fully accept that I called this incident completely wrong.
"Having adopted the position I did, it didn't allow me to gain the best view of what happened during the incident. It is clear that the goal should not have been disallowed."
Diamond was understandably enraged by the decision and could now face disciplinary action for his public criticism of Brines.
"I asked about him about the decision and he told me to go away.
"That angers a lot of players that you can't talk to referees. Especially him."