You could try the tax_query
with the 'NOT IN'
operator (untested)
$myposts = get_posts(
[
'tax_query' => [
[
'taxonomy' => 'post_tag',
'terms' => [ 'index' ],
'field' => 'slug',
'operator' => 'NOT IN',
]
]
]
);
where the taxonomy slug for tags is post_tag
.