Don't worry man I felt the same way when I first played Persona 3 on my PS2 (same with P3P). The game was so good that I just didn't want to finish it, but then I realised all the stuff you can do post game.
On a NG+ there are so many hidden stuff for you to do. For me particularly I like the ultimate boss battles that can only be done there. I don't want to spoil it for you but there is a certain character that you know who you can battle at the end of NG+. That person is the strongest opponent in the game, stronger than the canon boss and will require intense amount of preparation (several playthroughs even) and strategysing to beat. Plus in the hardest difficulty all I can say is good luck.
So yeah don't be shy to complete it and give it several playthroughs to unlock the real fun stuff. The game deserves it more than anything.
