Mills was disappointed to be dropped for the club's opening Premiership match of the season and says Reid is wrong to question his attitude.
"Within two months I've gone from starting a European Championship qualifying game for England to being completely omitted from the Leeds first team squad, so read into that what you will," Mills told his personal website.
"I find it a slur on my character that the manager has questioned my training and, in his opinion, I have not performed in matches or training.
"If I'm honest, I could have played better against Burnley and Shelbourne, but every player who featured in those games would probably say the same.
"Yet to suggest that my training is not up to standard I find very difficult to take."
Mills, who is in the England squad for Wednesday's friendly with Croatia at Portman Road, says he wants to help Leeds get back into Europe.
"I would love the chance to help put Leeds back to where the club belongs - at the top end of the table, challenging for European places," he said.
"This is a club I am proud to be at and I have no intention of leaving, despite the fact that it feels like I am being forced out.
"Once again it's up to me to change a manager's opinion and perceptions of myself. I am determined to force my way back into the Leeds squad and if and when I do get the chance to play in the first team again, I will seize that opportunity with both hands.
"I assure all the fans that I am here for the fight. I have proved people wrong in the past and I will do it again."