Yes, the intent most likely made the spell work. Everything made the spell work but the intention is the biggest part in almost every spell. You don't need meditation and visualization if you don't want too. Without your intention the spell has no reason and no purpose which would make it fail because it is useless and not really a spell.
There are different ways how people make spells. Some people might do what you did, some people might just write down their intention, etc. The list goes on as new methods are made and old methods are brought back up.