How can I deal with being turned down for a raise? I feel very unappreciated.

Could be for the first night, after that it does not matter

Look for other opportunities and come back to your boss asking if they can match that pay. If not, assess if compensation is your number 1 priority, if so, take the other offer.

Ask why, or ask how you can achieve what they feel would deserve the raise or move on to bigger and better things

Definitely ask for feedback from your manager about why you were turned down. As for clear goals / steps that you can take to have a raise be reconsidered in the future. If you're not thrilled with their answer then you'll want to look inward to see if you want to stay with your position.

Pay attention to the success (or failing) of the company and your part in it.

Tell them you’ll be looking for a new place where your efforts are appreciated.

Keep doing a good job and it will come or look for someone who will appreciate you.

Job hunt, unless there was solid good reason for no raise. Hunt, the company looks at you like a resource, do the same to a company.

Get a new job