well that you are a skilled player attests to why you were able to make it work. You happened to have a not so bad match up against annie as while she would bully you early on I imagine, once you got to 6 you could all in her without fear as your ultimate will cleanse her stun and nullify her ultimate and burst damage.
Imagine if you played this with old alistar where you could get free inch bane procs as you knock them away with W.
I have always felt that if you are the better player though, 99 times out of 100 you will win your lane if there is not heavy interference from jungle/other lanes.