Unfortunately the answer is "Yes." You always need to use a park ticket to get into any of the four parks, even if it is only for an Advanced Dining Reservation (ADR).
If you already have a multi-day ticket in the 4-9 day range, then it should only cost a few dollars to get an extra day added to the ticket, but in any other cases it probably won't make sense to pay for an extra day just to eat a meal.
If the cost of the extra park ticket is still a concern, then I highly recommend you look into changing your dining reservation to a location at one of the Disney resorts or Downtown Disney, where you won't need a park ticket. There are many options (including character dining) that are just as good, if not better, than the in-park dining options.
Hope that helps. If you have any follow-up questions, please feel free to submit them using the "ask Bret a question" link on this page.