The five returned late and drunk from an evening off during preparations for Chile's South American qualifiers against Uruguay on Friday and Paraguay next week, Borghi said on Wednesday.
Winger Jean Beausejour, reading from a statement by the five including midfielders Arturo Vidal, Jorge Valdivia and Carlos Carmona and defender Gonzalo Jara, said: "We did arrive back about 40 minutes late... a situation which is not right and for which we publicly apologise.
"We're not denying we took alcohol, because we were at a religious ceremony [baptism of one of Valdivia's children] common in our country. But Mr Borghi's assertion that we arrived in an inexcusable and inadequate state is not right."
Valdivia, Carmona, Beausejour and Jara held a news conference which was not attended by Vidal, who had returned to his club Juventus in Italy.
"We're extremely upset that Mr Claudio Borghi should make assertions like those he made," the players said.
"We cannot accept the remarks of Claudio Borghi that we got back in an inexcusable state. That's totally false. I feel quite hurt by Claudio's big lie yesterday," Valdivia added.
Borghi, who travelled to Montevideo on Thursday for the Uruguay match with his squad including five replacements, had said: "They were in no state to defend themselves."
Winger Beausejour added that Borghi, Chile's second successive Argentine coach after Marcelo Bielsa, refused to speak with the five players.
Chilean Football Association president Sergio Jadue asked for cautionary sanctions for the five players.
It is not the first time Valdivia and Beausejour have been reported as behaving badly. Media reported before Chile's match against Argentina in Buenos Aires last month that the pair had been warned for indiscipline although Borghi denied it.
Valdivia was punished for his part in an act of indiscipline by seven players at the Copa America in Venezuela in 2007. They were suspended for 20 international matches for being drunk and molesting a hotel maid. Five of the seven, including Valdivia, later had their suspensions reduced by half.
In 2006, Mark Gonzalez and Reinaldo Navia, who was also involved in the 2007 incident, were found with drink and women in a Dublin hotel during a Chile tour.
Chile, who lost their opening qualifier 4-1 to Argentina last month before bouncing back to beat Peru 4-2 at home, host Paraguay in Santiago on Tuesday.
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