Having grown exasperated by Miller's repeated failure to arrive on time for training, Keane decided he had no alternative other than to invite offers for the midfielder.
"Wednesday's decision is very disappointing," McLoughlin told The Independent.
"We accept that Liam was late three times in the past week but on two of those occasions the situation was out of his control - one of these was a well-publicised incident on the A19.
"The implication is that Liam is indisciplined and not fully committed to his job at Sunderland. I do not want to start a public row with the manager but I can't let that pass.
"Liam is not unprofessional and I think people who know him know that. In 18 months at the club Liam has been late seven times, most by a matter of minutes. The latest was half an hour when Liam and Stephen Elliott got a training session start time wrong last season.
"Liam is not casual in his approach to his profession and for the sake of his career, we need people to know that. Liam's disappointed not least because it damages his reputation in the eyes of fans at Sunderland and beyond.
"Another damaging thing is that the club's website yesterday referred to repeated warnings that Liam was given about timekeeping, but that is not correct. If the punishment fitted the crime Liam could accept this more easily, but he doesn't think it does.
"He'd still love to play for Sunderland but that is not his decision."