Interception in endzone = safety?

So,

There was six seconds left on the clock and the other team threw a Hail Mary. I intercepted it in their end zone, was instantly tackled (still in their end zone without leaving), and it counted as a safety for the other team.

Since the clock was at 0:00 I lost 5-3. It should have been an interception to go into OT.

... Or depending on the programming an interception for a touchback, then would read the clock at zero and start overtime.

...sigh