This phrase basically means that a statement is not true. In the example above, the statement "we need some more food" is not true.
You use "it's not like ___" when you want to give a reason for doing or not doing something. For example, if you're trying to convince your parents to let you borrow their car for the weekend, you can say:
It's not like I'm a bad driver or anything.
For another example, if a family member is telling you not to eat fast food, you can say:
It's not like I eat fast food all the time.