The club could decide to punch women as soon as this spring, he said.
Carlock said the possibility that some Fly members could resign in the wake of the vote "would be a tragedy--in my mind."
Graduate President of the Fly Eric E. Vogt said Sunday's vote is not a "final" decision.
"This is a step," he said. "We are working for unity, not to divide a community."
Vogt said he doesn't mind forfeiting University recognition, which the club lost because of its single-sex policy.
"I have experienced being recognized and not being recognized by the University and I can't tell the difference--with the exception of free heat," he said.
Carlock said the Fly would like to be the first final club on campus to admit women, but that will not influence its decision.
"Considering our history, it is appropriate we'd be the first," Carlock said. "If we were the first, we would have a monopoly on the female population [on campus]."
Winters said she thinks the club has missed a "golden opportunity" by deciding against a co-ed punch this fall.
"This was the best time, it is unlikely it will pass in the future," she said.
Carlock said he hopes groups like WAC will "respect what we've done so far and what we're going to do."
"We're trying not to politicize the issue," he said. "We are just a social club.