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The 34-year-old defender, who is the club's longest-serving professional, recently pressed the players' case for a £20,000-per-man bonus, to which they felt entitled after qualifying for the UEFA Cup.
However, Bates insisted that this was only due to them if they had qualified through the Premier League and not as FA Cup runners-up.
The Chelsea chairman sought to defuse the row in his programme notes before last Saturday's game against West Brom.
"Not unusually, Chelsea have been making headlines over the past few weeks. Graeme was unfairly singled out for criticism over the UEFA Cup bonuses that never were," wrote Bates.
"It was a misunderstanding that was taken out of all proportion and Graeme took the stick despite the fact that he was merely a spokesman.
"It was a classic case of (verbally) shooting the messenger. Graeme is, and always has been, a loyal servant to Chelsea Football Club."
That, however, has evidently not proved enough to change Le Saux's mind about stepping down, although he may still be involved on the players' committee along with the likes of Marcel Desailly and Gianfranco Zola.
Professional Footballers' Association chief executive Gordon Taylor revealed: "As a PFA delegate, you are in the firing line.
"There have been a few problems at Chelsea recently and Graeme has been speaking as the players' representative on these issues.
"Sometimes, these things can become personal, as has happened to me in the past. On your own, you can become the butt of any recriminations.
"He just feels that he wants to come out of the firing line. It will be better for both the club and the players to rely on their players' committee, rather than just one individual, from now on.
"That is much safer to avoid any personalisation. Graeme has been an excellent delegate for a number of years now and has his own career to think of.
"He speaks his mind very articulately and we would like to thank him for all of his hard work and wish him well for the future."