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'
)
)
);