How many epochs did you train the network for?
I think this is just overfitting. Normally you should use the validation error only and never look at the training error. When your validation error does not improve you stop training (that’s called early stopping).
The only time you look at the training error is at the very beginning to make sure that your network is able to overfit your dataset (i.e. learn to represent completely the dataset).
If it does not overfit, change your network or preprocess your data because your network isn’t able to learn anything.
If your network is able to overfit, great, now you can focus on having it learn a general representation. You discard that training error and only focus on validation error which corresponds to unseen data.