Burnley forced to put frustrations aside after first defeat in five games at Leeds United
The Clarets were on the wrong side of two game-changing decisions at Elland Road as referee Robert Jones awarded the hosts a controversial penalty before chalking off what would have been a Burnley equaliser.
Jones - taking charge of only his fourth Premier League match - then blew the whistle to deny Barnes his second goal in as many games after Illan Meslier had collided with Mee inside the box.
"We had a few good chances, a few decisions went against us, we'll have to fight again," Barnes reflected post-match.
Asked about the incident that saw play stopped before his effort, he said: "The keeper tried to smash Ben Mee, missed the ball and I put it in. I don't know why it was ruled out. There were so many decisions all day, it's frustrating.
"In the second half we were a much better team. We have got plenty more games this season."
Burnley skipper Mee echoed his teammates thoughts.
"I don't know how it's a foul against me, " Mee said.
"If anything, don't give anything - it's more of a penalty than a free-kick. Barnsey put in a good finish, but I don't know what he [the referee] was doing."
He added: "Frustration, decisions didn't go our way today. We started slow, didn't have the best first half but stuck in there and came out to give a good performance."