"I don't share this gentleman's opinions, but we have to be tolerant and respect everyone's opinion," Keysi Sayago, 23, told a press conference in Caracas a day after being crowned Miss Venezuela 2016.
Machado, who was Miss Venezuela in 1995 and Miss Universe the following year, has surged into the spotlight of the US election since Democratic nominee Hillary Clinton named her as an example of her Republican rival's mistreatment of women.
Machado accuses Trump, who formerly owned the Miss Universe pageant, of verbally abusing her during her reign.
She says the billionaire real estate magnate called her "Miss Piggy" over her weight and "Miss Housekeeping" because she is Latina.
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The polemic later escalated into a late-night Twitter tirade by Trump, who trashed Machado as "disgusting" and urged voters to "check out (her) sex tape and past."
Pressed by reporters, Sayago avoided wading into the dispute, but repeated: "I don't share (Trump's opinion), but I respect it."
Venezuela, a major oil exporter, has been hit by severe shortages of food and basic goods as global oil prices have plunged since 2014.
"It affects all of us. We haven't been spared. But we've tried to keep ourselves in a bubble, because at the end of the day this is a beauty pageant," she said.
"We couldn't let ourselves get swept up in all the bad things. This gave the country a reason to smile."