Can I refuse new job responsibilities if I am denied a raise?

I've been working at this place over 2 years now, and have taken on at least two responsibilities that come with a title. When I was up for review I asked for a very fair raise because of these additional duties, and because I've been an amazing employee (I've been told this, I don't just have an ego). I was denied my raise request and given just what would match inflation. I'm now regretting taking on the job duties and feel that if they don't want to pay me for extra work then I won't do extra work. Am I being unreasonable? Is there a way to approach this with my boss without totally screwing myself? Any and all thoughts are welcome, I'm only beginning to learn how to stand up for myself and I'm afraid of taking it too far.

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