That's because it's a PG-13 golden-age gee-whiz action movie. There's not supposed to be any indications or implications of sex onscreen. But what happens offscreen is entirely open to speculation.
And yes, you could speculate that Steve Rogers was as chaste as Galahad, if you prefer. But you could just as easily speculate that he, like any other soldier of the time, had plenty of access to prostitutes and nurses and other willing women every time he went on leave for a little R & R. (Or you could try an entirely different tack, and go with the long-running innuendo about Cap and Bucky...at least in the film universe, Steve wouldn't be a pedo.)