On John 3:5

"Jesus answered, Verily, verily, I say unto thee, Except a man be born of water and of the Spirit, he cannot enter into the kingdom of God".
This verse means that in order to "enter into the kingdom of God", we must be baptized and given the Spirit, or the gift of the Holy Ghost.
Now, I don't know a whole lot about being "born again" and "saved", as it relates to different denominations. As far as I know, Latter-Day Saints, Catholics, Baptists, and some other mainline Christian denominations believe that you need to be baptized. The methods are different (sprinkling as opposed to immersion), but the idea is still the same: being born of water.
So, how are some considered "saved" and "born again" by simply proclaiming belief in Christ? "I prayed to God, told Him I was a sinner, and that I wanted to be saved. So I invited Him into my life and I've been saved ever since." How is that justified if the Bible states that you need to be baptized in order to be accepted into the kingdom of God?
Please, don't point out other doctrines and ask me about them, especially in regards to LDS doctrine. That is not the point. Please stick to the question at hand.