It is true that a large part of the Croatian economy is dependent on tourism, and English (despite not accounting for the majority of the tourists) is widely spoken.
It is also true that in major towns like Split or Dubrovnik, almost everyone (in tourism) speaks English up to a point.
That said, you don't need to travel far for English to be less widely spoken, and speaking a few Croatian phrases can be incredibly useful.
Picture the situation where you desperately need to order a glass of red wine Čaša crnoga vina ...
... and you can't.
Is there more that needs to be said;)
Italian an official minority language in Croatia is also widely spoken, so in the unlikely situation above you could try some Italian.
See also Food and drink. 2, Food and drink. 3 and Croatian holiday phrases.