Prayer may be an essential part of recovery for some people, but to say it is true for all would be silly. There are people all over the globe (and all throughout time) who do not pray and they successfully quit drinking.
Note that there are also very religious people who use prayer in their daily lives, but chose to end their addictions secularly. This is more common than people think. It is a misconception that everyone who chooses secular recovery is an atheist or agnostic. Many very religious choose a secular road.
I think something more important to ponder would be: why does what others think affect you so strongly?