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."
"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.
'NO STATE'
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.
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.
