Return rows in Table 1 where joined table 2 is missing a value

Question

I need to return groups where Items.value DOES NOT equal ZZZ in that group at all. I tried joining Items on group where items.value <> = 'ZZZ' but it still returns goups that have items with ZZZ. I also tried adding a sub select where selecting items.value = 'ZZZ' not exists but that didn't work either.

Groups
+----+------+--------------+
| id | name | TAG          |
+----+------+--------------+
| 1  | AAA  | 1            |
+----+------+--------------+
| 2  | BBB  | 1            |
+----+------+--------------+
| 3  | CCC  | 1            |
+----+------+--------------+

Items
+----+------+--------------+
| id | Value| Group_id     |
+----+------+--------------+
| 1  | XXX  | 1            |
+----+------+--------------+
| 2  | YYY  | 1            |
+----+------+--------------+
| 3  | ZZZ  | 1            |
+----+------+--------------+
| 4  | XXX  | 2            |
+----+------+--------------+
| 5  | YYY  | 2            |
+----+------+--------------+
| 6  | ZZZ  | 2            |
+----+------+--------------+
| 7  | XXX  | 3            |
+----+------+--------------+
| 8  | YYY  | 3            |
+----+------+--------------+
| 9  | OOO  | 3            |
+----+------+--------------+

Query on above should return

Group
+----+------+--------------+
| 3  | CCC  | 1            |
+----+------+--------------+

This does not work. It returns Groups id 1, 2, and 3.

SELECT * FROM Groups g
WHERE NOT EXISTS (
  SELECT 1 FROM Items as i
  WHERE i.group_id = g.id
    AND i.value = 'ZZZ'
);

How do you select all the groups above that have 'ZZZ' in Items and then determine which group_id were excluded? -> 3