^^^He didn't need to, it was clear that May was supposed to have figured it out.
Yeah, that conversation in May's back yard while she's packing up her stuff to move (SM2) really makes you believe she knows.
One thing about Peter Parker in all four Spidey films: Peter periodically does not-so-bright things. But in the character's defence he is supposed to be a kid, a young adult, and they're prone to having less-than-bright moments. Hell, there are grown adults who are supposed to know better that do stupid things all the time (collectively speaking).