Picard's infamous First Contact quote suggests no money but in practice, any economy requires some means of exchange. Whether it's real or virtual currency, or some other token, or even some kind of impromptu ad-hoc barter system, there has to be some means of converting one resource into another in a moderately culturally-durable way.
This wouldn't be the case if resources had no value (i.e. no energy required to create them), but we consistently see that despite fusion/warp power, transporter/replicator tech, etc, etc, resources still retain a value. It's a mere fraction of what they would cost without those advanced technologies, I'm certain, but a cost remains attached to them.
(An example of a society where money truly wouldn't be required would be the Q, where matter and energy are transmutable - and perhaps can even be created or destroyed with no regard to overall entropy - solely through thought).
While a resource has a value, the process to create it also has a value, and so does the time commitment of those involved in its creation. How you measure that value (i.e. whether something called "money" is used to translate things from resource to resource) is somewhat irrelevant. It only influences the economic efficiency of the translation process (money is a lot more efficient than bartering).
It's possible that the internal Federation economy takes this efficiency even further and trades actual energy requirements around, rather than using money as a proxy to measure those requirements. If you can measure energy requirements sufficiently accurately, you can value things based on the energy required to create and maintain them, and the energy required to keep someone fed & sheltered. Highly valued people would accrue extra energy resources, permitting a more luxurious lifestyle.
Technically, this system wouldn't be using money - in this scenario, a currency is not needed to generate accurate comparisons of value - so is consistent with Picard's statement. But in practice, it's simply a more efficient monetary medium (again money simply being a way to assign consistent values to permit comparison).