More layers in NN give worse result
Maybe you are making a mistake, put your code here. But without seeing your code, these are possible points:


Vanishing problem, I don't think you this problem due to having a very shallow network. You can change your activation function to relu for avoiding that.
Covariat shift, What it means is that similar to input features which have to be normalized, the inputs of the deeper layers have to be normalized to. The normalization process is in a way that the inputs to each layer should have a special distribution that does not change. You can use batch normalisation for avoiding that problem. 
Bug in coding, you may have fed the activations of each layer to the next layer in a wrong way or you may have updated the weights not simultaneously If you have not used vectorization. There are also numerous different reasons which may lead to bugs in your code. 
The number of neurons may not be enough for each layer, try to increase them. For understanding the meaning of increasing the layers and the number of neurons in each layer, you can take a look at here.