At the point someone has called you out for being sexist, the relationship you should be focused on pursuing is the one with the next person, because your shot with this one is gone.
Yes! And if you're so worried about how "technical" you'll sound when asking for feedback (which you may or may not get - nobody's entitled to give it), you also miss out on the potential to get some data points to refine your approach in the future. Sounds like a good opportunity to repeat that same old mistake all over again and write it off as "I just wasn't flirty enough." Not the problem, never was the problem.