If you put the constants/subs to be exported into @EXPORT_OK, they will only be exported to the caller's namespace if the caller requests them on the use line:

use MyConstants qw/LOGIN PASS IP DB_NAME/;
...
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Note: I've renamed your package to MyConstants. Two reasons:

1. All lowercase package names are notionally reserved for pragmas (system defined packages).
2. constant is already used for the pragma you are using to define your constants.

If you are sure that you always want to export those constants, then you can alternatively add them to @EXPORT, and they will exported into every namespace that uses the module. This is vagely frowned upon as it doesn't give any clue as to where they came from in the calling code, but in the case of constants and a package called MyConstants or similar, it would probably be acceptable to most people. Expecially if there are a lot of constants that will usually need to be imported.

Update: Corrected s/@EXPORTS/@EXPORT/ courtesy of ysth.