public static String escapePath(String path)
{
    return path.replace("\\", "\\\\");
}

The \ is doubled since it must be escaped in those strings also.

Anyway, I think you should use System.getProperty("file.separator"); instead of \.

Also the java.io.File has a few methods useful for file-system paths.

In cases of strings and escapes you should really show your actual code, an MCVE, not explain your code. Special char in regex: one backslash, actual backslash in regex: two backslashes, two actual backslashes in regex: four backslashes. Regex in java string: double all the backslashes.

Therefore one literal backslash means two backslashes to represent it in a String, means 4 backslashes to represent in a regex String. All "regular" special chars of regex like \w need two backslashes in a java String as well -> "\\w".

It looks like your have exactly double the amount of \ you should have in the regex. Only if you have a regex String and want to match a literal \ four backslashes are correct.

Note regarding your code: you write:

String targetStr = someMethod.get(); // value is C:\\my\\drive\\application\\webapps\\ROOT\\classes\\there\\is\\a\\clazz

But that is not entirely correct, the value is

C:\my\drive\application\webapps\ROOT\classes\there\is\a\clazz

Only because your IDE displays it as a String it escapes the escape character \ and shows double \\. If you would check the characters it has there is only one '\' between every two path components.