No you don’t. While the rehearsal dinner is a lovely tradition, don’t feel obligated to host one if you can’t afford it.
You can still have a rehearsal even if you don’t have a rehearsal dinner. Make it clear to your bridal party that after the rehearsal everyone is on their own for evening activities. You don’t have to share that it’s a budget issue. If you’re not sure what to say you can explain that you have too much to do the night before the wedding and decided not to have one.
And even if you make it an early night you can invite a few girlfriends over to spend the night and make it an old-fashioned slumber party.