No need to correct explicitly, but ensure you include title (Mr/Ms/Dr/Prof./&c.) in your signature
To an outsider, it is often unclear:
whether the designated contact is an academic or an administrator; and
whether the designated contact has a doctorate (in the UK, many people working in academic administration do have a doctorate).
The lack of clarity is exacerbated by the fact that many university websites and web profiles do not spell out titles and credentials prominently.
Given that it is a far bigger faux pas to address somebody with a doctorate as Mr/Ms/&c. than it is to address somebody without a doctorate as Dr/Prof., the general advice for an outsider is, "if in doubt, assume the designated contact has a doctorate".
If you are concerned about anybody being misled, the best solution is to ensure your electronic-mail signature includes your title, credentials, and position; for example:
Ms Josephine Bloggs, BA (Ebor.) MA (London)
Secretary for Research and Postgraduate Programmes, Department of Futile Studies
University of St Kilda
+44 1632 960555 [this is a fictitious number, so calling it would not disturb anyone]
But if it really bothers you that much, you could add a brief note just below the salutation in your reply; for example:
Dear Mr Schopenhauer,
[Please note that I do not hold a doctorate, so I am "Ms Bloggs"]
Thanks for your enquiry about our postgraduate programmes. We are certainly willing to consider applicants with a degree in a different subject, and your background in philosophy looks like it would be compatible with the prerequisites for our Master of Futile Studies programme. I should observe, however, that it is very windy on our campus, so your proposed enquiry into whether a falling tree makes a sound may be tricky to ascertain reliably. We should also warn you that, in order to avoid replicating the mistakes of Easter Island and Donal Rusk Currey, we have a rigorous policy to protect the trees on our campus, and you will require a special permit and ethics approval to fell any of our trees for research purposes. You may find it helpful to make a campus visit before committing to your project.