As your error message clearly states, this is not a Perl problem.
If you try and run your statement:

INSERT INTO usrTEST.test_table('id_oggi') VALUES ('111111')

in the sql query analyser, you will find it fails with the same error.

I suggest you look at the documentation for a SQL insert statement - you'll see that you shouldn't quote the column names. Try this instead:

INSERT INTO usrTEST.test_table(id_oggi) VALUES ('111111')

When you've got it working in query analyser, then you can put it into you Perl script.
A side point: you don't need to escape single quotes with \ in a double-quoted string.