Your regex should cover your whole string, by using ^ and $ to signify start and end of string:
/^[abcdefghijklmnopqrstuvwxyz]+$/
Otherwise, it will match part of your string, which is why it matches when you have a mix of good and bad characters, but fails when every character is bad.
You can shorten the regex by using a character range like this:
/^[a-z]+$/
You can use this online tool to build and test your regex.