The Northern Ireland international, who was handed the captain's armband for Saturday's 3-2 win against Blackpool in the absence of dropped keeper Scott Carson, could not hide his dismay that Scharner publicly said the players had become "lazy" after the club's internal fines system was scrapped before Christmas.
However, after boss Roberto Di Matteo confirmed that the Austrian international would not face any punishment for his outburst, Brunt called on the rest of the squad to put the matter to bed.
"We saw the comments and it's disappointing that they were not made to the players," Brunt said.
"Maybe he thought it would get a reaction and if he feels happy with that it's fine. That's his judgment."
He added: "We were a little bit disappointed but things are said and we will draw a line under it.
"People fall out on a regular basis in training and in games. That's the nature of football and I don't think anybody will have any problems."