You can apply $in or $nin to your queries if you want to use "not in". In MongoDB, you can also use the NOT EQUALS operator, $ne, to get what you want as it uses the value that cannot be searched, refer to the following command:
db.myCollection.find({'blocked.user': {$ne: 11}});
If you want multiple values then use $nin:
db.myCollection.find({'blocked.user': {$nin: [11, 12, 13]}});
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