Controversial striker Teo Gutierrez left Racing with nine men for the last 21 minutes after his dismissal for apparently insulting the referee. He was later alleged to have confronted team-mates with a paintball gun after a fight in the changing room.
Basile, a former Argentine, South American and World Club title winner with Racing as a defender in the 1960s, took charge in January but failed to bring the best out of a talented squad with only two wins and three draws in 10 Clausura championship matches.
"After taking a few hours to think about it, Alfio Basile decided to resign as coach of the club's first team along with his coaching staff," Racing said on their website on Sunday.
Basile, who had supported the problematic Gutierrez and pinned his hopes on the Colombian leading Racing's title challenge from the front, had been quoted as saying in the heat of Saturday's result: "No way I'm staying."
The 26-year-old Gutierrez scored the opening goal in Saturday's defeat but it was only his third of the championship, taking his league tally in 14 months at Racing to 20.
Unconfirmed media reports said there was fighting in the Racing changing room at Independiente's Libertadores de America ground as the players turned on the talented Gutierrez for another senseless red card, his second of the year and fourth in Argentina.
Basile's assistant Claudio Ubeda, speaking to Fox Sports on Sunday, said: "What I experienced in the changing room I've never experienced before in my career.
"Regardless of the fact Teo is a good footballer, measures must be taken or there will be problems with the whole squad major surgery is needed. If I had to take a decision, Teo Gutierrez wouldn't play for me again."
However, at 68, he may now throw in the towel. He had been out of work for more than a year when he took the Racing vacancy following Diego Simeone's departure to Atletico Madrid in December saying it was out of love of the club he supports and a desire to make the fans happy.
