Start with a thick white sauce (same as bechamel sauce) and that will give you the consistency you need.
And if you beat potatoes to much they become mushi and glueis.
Now if you still have the croquette dough that you initially prepared, don't throw it away. Add flower to the right consistency. And a little salt and pepper because you will loose some of the potato flavor by adding to much flour.

I agree that the oil is probably not hot enough. It should be about 375F degrees (190C). But possibly your potatoes were still wet when your formed the croquettes.

I'd bet the heat isn't hot enough. You want a hot pan, oil almost smoking.