I guess, there is no exact way of retrieving the time only when the post's content is updated until you change the core functionality of wordpress and that might lead to some other issues. But here is a workaround I would like to propose here.
You can retrieve the time/date only when content is updated via revisions.
A revision is created only when you change the content of the post, not otherwise.
But there is no exact way of retrieving only date/time but a set of parameters.
Use this code and it'll give you a string that contains the required data:
What you can do now is fetch the complete string in a variable and use regular expression to extract the desired stuff.
Reference: Codex link. Nut nothing much is available here.
EDIT: (thanx for the function update)
This is the code based on
wp_post_revision_title() and working as expected.
$revision_data = wp_post_revision_title( $post ,false );
$date_time = explode('@', explode('[', $revision_data));