There are two kinds of happiness in Civilization V -> local happiness and global happiness.
Global happiness is the number displayed at the top of the screen. It is the sum of the local happiness of each city, plus any global happiness generated by other means (such as wonders, or luxury resources, as each unique resource generates global happiness).
Local happiness is the happiness generated by one specific city. This number can never increase past the size of the city (so a 6 population city can only generate 6 local happiness, regardless of how many happiness generating structures it builds).
Stadiums and Colosseums increase local happiness, which is why you did not see your happiness value change when they were built.
Some buildings (generally wonders) directly increase global happiness, without caring about the population size of the city they are built in. The Notre Dame wonder is an example of this.