Once the Bill of Rights was added, the Constitution did at least something to address the concerns of all citizens (except, perhaps, for women and non-whites). However, it did more to address the concerns of economic elites than those of other people.
The Constitution was a Federalist (as opposed to an anti-federalist) document. It gave more power to the central government and isolated the government from the people. This was something that the Federalists (economic elites) wanted very much.
The concerns of anti-Federalists were met, to some extent, by the Bill of Rights. The anti-Federalists were concerned that the central government would tyrannize them. By creating the Bill of Rights, the Framers were able to allay these fears to some extent.
In this way, the Constitution did at least something to address the concerns of both Federalists and anti-Federalists.