That would pose a problem, since the 14th Amendment was passed in 1866. The Civil Rights Act of 1871 gave rise to the 15th Amendment.
The Civil Rights Act of 1871 was enacted by Congress because some of the states were ignoring the requirements of the 14th Amendment. It did not have anything directly to do with the 15th Amendment.
The Civil Right act of 1871, now codified as Title 18 US code 241/241 for criminal purposes and 42 US code 1981-1988 for civil remedies, is the enforcement mechanism by which citizens of states can seek relief from violations of the 14th Amendment. It's a bit more complicated than that, but this is a good general explanation.