The Mexican Football Federation's (FMF) national teams director Nestor de la Torre, who also fined another 11 players after the squad held an unauthorised party following a friendly, handed in his resignation on Monday.
The 13 players sanctioned on September 13, most of them members of Mexico's World Cup squad in South Africa this year, asked not to be picked again for the national team until the FMF had made changes in management, an implicit demand for the unpopular De la Torre's resignation or dismissal.
The 11 fined players were nonetheless named last week in a squad for Tuesday's home friendly against Venezuela in Ciudad Juarez.
"In an attempt for regulations to be respected and applied, it became clear some (people) were made uncomfortable... I'm stepping aside in order to be consistent," De la Torre told a news conference.
De la Torre, whom players have said was unpopular with them since he took his post in March 2009, had met with squad members on Sunday without success in an effort to try to resolve their differences.
"They wanted me to say sorry, a public apology for having applied the regulations, which I was not prepared to do," De la Torre said.
"No-one forced me to reach this solution (by resigning). I'm not prepared to accept conditions for national team selection or sit at a table and reach agreements."
British based forward Vela and midfielder Juarez were banned from the national team for six months for breaking four rules of behaviour while on international duty. World Cup captain Rafael Marquez was among the 11 players fined.
The party was held after a friendly against Colombia, a 1-0 win in Monterrey on September 7.
