I'd have to ask what passage you're thinking of. If you mean the Eucharistic formula quoted at Luke 22:15-20 and elsewhere, that's supposed to be the Passover meal, which, due to commandments in the OT, is supposed to include unleavened bread.

Also, ask r/AcademicBiblical.

Neglecting for a moment the cultural context and religious rules to follow with regards to food, people in biblical times didn't "use yeast" - they didn't even know it existed. Yeast was discovered to be the reason for fermentation in the 1850s. Before that wine was either produced by spontaneous fermentation - yeast accidentally enters the grape juice - or by spiking it with already fermenting wine. There was no connection made between the alcohol production in wine and gas production in bread.

Is there a particular passage you have in mind?