Can I put a postdoc as one of the references in my CV?
This depends on what is available to you. Yes, institutions value the opinion of well established researchers (professors), but they also value the honest opinions of people who can speak about your likelihood of success and how you "get along" in the research environment. The best are people who can do both, of course. 

But you don't want lukewarm praise from top people. So think about who you have as possible recommenders and what they might say. Then just make a decision. I doubt that it will matter in a critical sense, actually.