"it's too crowded" is the default message to say you've reached the happiness limit.
Depending on difficulty, the first few people in a city will be content. All the people who are born after that will be born unhappy.
It's 4 people in Chieftain, 3 in Warlord and 2 in Regent and Monarch and 1 on the rest...
You can make them happy with buildings, luxuries, money (luxury slider) entertainers (not recommended for a long term solution) and ehm... some other things.
So your problem is not overpopulation, but a lack of things that make people happy/content.
And yes, at the start of the game, building settlers and workers is a good way to keep the population down so you don't have to deal with it. But after that you can't get enough people. People work the tiles, worked tiles means production and money. Production and money means a military, science and progress.
Also note that your city will only 'shut down' when there's more unhappy people than happy people. So having 4 happy, 4 content and 4 unhappy in a size 12 city is good enough.