Should I send an email back after getting rejected for a Master Project?
You never lose by being polite - especially to people who can possibly help you in the future. I would suggest sending an email, or even postal mail - a bit more formal. 

The email/note should be short. Thanks for your consideration of my application. I appreciate your help and hope to be able to work with you in the future. 

If you need a project from another professor, you could also ask him/her for any advice or recommendations they might have. 

Don't burn your bridges. Don't let them fall into disrepair. Keep them tidy and well swept.