River beat Boca on Tuesday in the "superclasico", the biggest derby in Argentine football, leaving them 15th in the Apertura championship with 17 points from 14 matches and seven defeats.
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"After the match we (the coaching staff) took the decision not to be Boca's trainers any more," Borghi told a news conference.
"The results have not been as good as we all expected, players, directors, fans, coaching staff. There are more bad things than good on a sporting level."
Former Argentina striker Borghi, who steered Argentinos Juniors to the title in the previous Clausura championship and took charge of Boca in May, said he felt the club would benefit from a change.
"There's a saying that 'a debutant coach wins'. The one who leaves takes some of the pressure with him and the one who comes in arrives lighter," the 46-year-old said.
NO INTIMACY
Borghi was a member of Argentina's 1986 World Cup-winning squad and also helped Argentinos Juniors win the South American Libertadores Cup in 1985.
Many observers had wondered if he would stay at Boca until the end of the season in June and when Marcelo Bielsa quit as Chile coach two weeks ago, Borghi was linked with the job because of family ties in the neighbouring country.
"To be denying rumours ever day is tough. Boca is like making love with the window open, you don't have any intimacy," he said.
Borghi made his name as a coach in Chile, having ended his playing career there. He steered Colo Colo to four successive titles and the 2006 Copa Sudamericana final.
Youth coach Roberto Pompei will take charge of Boca as caretaker for the second time, after a spell of six matches at the end of last season.
Media reports said Julio Cesar Falcioni, who coached Banfield to their first Apertura title last December, was the favourite to take over on a permanent basis.
