In this article the author says
...without applying regularization we also run the risk of underfitting...
Why we might get underfitting without regularization? Regularization “make” network simpler to avoid overfitting and not underfittin. So, if we don’t have regularization it won’t cause underfitting.
We require regularization when our model is overfitting, i.e our training accuracy is considerably higher than our testing accuracy.
When our model is underfitting,we need to increase complexity of the model( by, say, adding new features).
Hence, Regularization is not a solution to underfitting , and that is what the author is trying to say.