Automation in Agile is very critical.
Think about the many features that are added and delivered to every Sprint. There has to be a way to make sure that the newly added feature is not impacting the existing functionality.
Due to the low Sprint duration, it is practically impossible to execute the entire suit every time the product is incremented at the Sprint ends. Having an automated test suit would definitely play a bigger role here.
However, introducing and maturing into automation would definitely take some time. Doing an initial investment in planning and designing the automation activity would definitely pay off in the long run.