On your resume and job applications, use the official title you've been given by the company so everything will match up and go smoothly when your references are checked and your employment is verified by potential new employers.
On your resume, when you highlight in bullet points your accomplishments based on the duties you performed in the position, be sure they are accurate and do not worry that the accomplishments might not fall under the purview of employees with your (incorrect) title.
In any cover letters that accompany your resume, you could address it simply (and then move on, not dwelling on it), such as "Although in my previous position I held the title of 'Web Developer', I did not perform traditional web development but was in fact responsible for system administration duties such as ..." How you frame this job will depend on whether or not you are looking for something in web development or systems administration (or both).
Finally, I agree with what HLGEM said about clarifying your title in parentheses if you really feel it is warranted. For instance, I was once officially a "Systems Engineer V" but my actual working title was "Chief Architect and Manager of Software Development". For verification purposes, I would use the former, but I would also parenthetically note the latter, as it is so vastly different.
Your overall goal should be to represent your skills and experience appropriately on your resume, augment this information through your cover letter, and provide verifiable information on your resume/applications to ensure the process runs smoothly.