A picture would really help but it might be a simple patch job. Sail tape won't work long term (i sail...tape is for emergencies and doesn't hold much tension). If a sail tears, depending on the material and age, it's either a replacement or a sewn patch. You can sew around the sail tape and it might work.

If I'm understanding your description, a sewn in doubler patch might take care of it and still look good if you do it right. A pic would help to better understand your rip.
On a home made hammock/tent/tarp, a tear is sometimes a blessing as it exposes an unforeseen stress point, leaving you with a better product once repaired.