How do I correctly use "Not Equal" in MS Access?

Like this

SELECT DISTINCT Table1.Column1
FROM Table1
WHERE NOT EXISTS( SELECT * FROM Table2
    WHERE Table1.Column1 = Table2.Column1  )

You want NOT EXISTS, not "Not Equal"

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By the way, you rarely want to write a FROM clause like this:

FROM Table1, Table2

as this means "FROM all combinations of every row in Table1 with every row in Table2..." Usually that's a lot more result rows than you ever want to see. And in the rare case that you really do want to do that, the more accepted syntax is:

FROM Table1 CROSS JOIN Table2

In Access, you will probably find a Join is quicker unless your tables are very small:

SELECT DISTINCT Table1.Column1
FROM Table1 
LEFT JOIN Table2
ON Table1.Column1 = Table2.Column1  
WHERE Table2.Column1 Is Null

This will exclude from the list all records with a match in Table2.