The reason for this is that "true equality" is not just a legal concept. It also involves elements of economics and social attitudes. Legal equality can be mandated by law. Economic and social equality cannot be in any effective way.
After African Americans became legally equal, there were still all sorts of sources of inequality. Many adult African Americans were still poorly educated and good jobs for uneducated Americans were starting to slip away. Many young African Americans were still going to substandard schools. It is very difficult to remedy this by law because it would take, at the very least, either large sums of money or forced integration. Neither of those is politically easy to accomplish and it's not clear that they would bring educational equality anyway.
The civil rights legislation could not make African Americans economically equal to whites. It could not prevent some whites from having racist attitudes and it could not prevent blacks from having their attitudes affected by a "culture of poverty." For these reasons, legislation was not enough to bring true equality.