I don't really have any advice, my 5 year old still needs help going to sleep, but our girls (my DD2) are nearly exactly the same age (mine is 2 days older) and she gets DH to pat her to go to sleep.

I don't pat her though, I sit in there on her bed, and be firm (but not angry) that I'm not going to pat her to sleep, but I will stay in the room until she falls asleep. If she gets upset, I just remain calm, and keep reassuring her that I am helping her to go to sleep. So you could try something like that - I find that I have to rock DD3 to sleep during the day while sitting on the bed trying to get DD2 to sleep, and if she wasn't used to me not patting her, then I would have serious issues too.

But if you ever find out the secret formula to getting them to fall asleep on their own - let me know! LOL