Hugs hun, very frustrating. But as you have already said she is still tiny.
There are a couple of methods you could try.
Firstly though, you need to be putting her down awake. Weither its fully awake or very nearly asleep (which is prob the best option right now)
You can put her down, and pat/rub her in a nice calming rhythmic pattern. (Aston she gets used to this you progress by keeping hand still, and then moving hand away) and saying shhhhhh, which enables her to hear you yet, its calming and will help to soothe her. Don't pick her up, unless she's very distressed, and just continue your sootheing. Will take longer to begin with but she will get used to it.
Or you can put her down (very nearly asleep) and leave her until she becomes upset. Pick her up. As soon as she stops crying. Put her back down again. Becomes upset, pick her up. Calms down, put her down etc.
Personally I prefer the first method, but its very much .personal preference.
HTH