Exclude post format from get_posts

You just need to set the operator parameter to 'NOT IN' (see Codex on tax queries).

Untested, but for your purposes:

$args = array(
    'post_type'=> 'post',
    'post_status' => 'publish',
    'order' => 'DESC',
    'tax_query' => array(
        array(
            'taxonomy' => 'post_format',
            'field' => 'slug',
            'terms' => array( 'post-format-aside' ),
            'operator' => 'NOT IN'
        )
    )
);