The Wales captain was insulted by a group of supporters as he left Madrid's training ground after returning from international duty injured last week.
Asked if he felt the media and fans were being unfair with Bale because of his injuries, Barnett told reporters: "It's irrelevant. I don't care what they think.
"Why should I care? I think they've been disgusting to Gareth Bale."
Bale was criticised by the Spanish media for choosing to play for Wales in the last international window despite being unavailable for Los Blancos this season. Bale, 32, has not featured for Madrid since Aug. 28 because of a hamstring injury.
He did start, however, for Wales in a 5-1 win over Belarus in a World Cup qualifier on Nov. 13, in what was his 100th appearance for his country, but was replaced at half-time due to injury.
Three days later, Bale was in the stands at the Cardiff City stadium in Wales' 1-1 draw against Belgium before returning to Madrid to begin treatment.
Real Madrid manager Carlo Ancelotti denied there is any friction with Bale and said: "He was cleared to go, they assessed him and then he played and got injured.
"Perhaps the assessment wasn't quite adequate and now our idea is to get the player back because we want him here and believe he can be useful for our team this season.
"We have to do things right so we can get him recovered and back with the team soon. Together, we'll do all we can because it's not true we're at odds with him. We'll try and get him back as soon as possible.
"Bale, as a Wales player, obviously has a special affinity for his national side, but he wants to play for Real Madrid whatever happens as well. He can't wait to be back playing."