His presidential plane arrived home in Bolivia's capital early on July 4, following an unplanned 14-hour layover in Vienna.
His government said France, Spain, and Portugal all refused to let it through their airspace, forcing it to land in Austria.
Austrian officials then reportedly searched the aircraft unsuccessfully for Snowden, the former IT worker who is seeking asylum in Bolivia and a handful of other countries to avoid extradition to the United States following his disclosure of classified elements of U.S. electronic eavesdropping practices.
Morales told supporters gathered at the airport that some European countries should free themselves from the United States.
His government has claimed the U.S. government was behind the incident.
U.S. President Barack Obama has warned giving Snowden asylum would carry serious costs.
Heads of state in the 12-nation South American bloc Unasur denounced the "unfriendly and unjustifiable acts" and called a summit in Bolivia to discuss the matter.