Validation accuracy is always close to training accuracy
The fact that the training accuracy and the validation accuracy are close it is nothing to be concerned about. As you mention, it means your model are generalizing well.

The thing to be worried about is the low training accuracy. It seems that your model is under-fitting the data but with low variance. This is the typical scenario of a model with high bias and low variance.

The bias is the error (whatever you measure this error) in your training data. It tells you about how well the model is forecasting with seen data. High bias means poor performance (under-fitting). The variance is the difference in performance between the training data and the validation data. If the differences are high (far better performance in training than in validation) the model has high variance (over-fitting).

Typically, decreasing the bias implies increasing the variance (bias-variance trade-off) then, probably, as you get better results in training, the validationa ccuracy may decrease. But, if the model is well designed, you may end up with low bias and low variance.