Shouldn't be rubbery....but soft and tender....sounds like instead of potato puffs you made pasta with potatoes.
I think there was too much flour and not enough potatoes.
When I make gnocchi I boil about 1 1/2 pounds of russet potatoes, peel and put through a ricer....beat an egg and add about half of that to the potatoes.....mix and start adding flour, gently mixing.....when the mix is no longer sticky and you can form it into a roll, it's done. I use about half as much flour as potato.....but every potato is different, some drier than others.
And don't forget salt in the mix....and pepper if you like....and perhaps some grated parm cheese....

Thanks for response. My mixture was quite sticky. From your advice, I think I'll change the flour/potato ratio and see what happens. "Pasta with potatoes" does kinda sound like what I did.

Thinking maybe flour should be semolina, too. Does that make any sense?

I think you might also be cooking them too long. Take them out within 10 seconds of when they pop back to the surface.

Don't use semolina.....you don't want a "hard" flour....pastry flour would be OK I think.
Don't think they were cooked too long...in my experience, if you cook them too long they fall apart.

Here is a link that might be useful: gnocchi like an Italian grandmother

Interested in the flour idea. I used King Arthur unbleached white bread flour.....perhaps too glutinous for this purpose? (and likely too much of it compared with the potatoes) My dough certainly was sticky/stretchy/gummy.

@Lindac....thanks for this link. Haven't read the whole thing but had to laugh with relief at this line: "Gnocchi recipes aren't for the faint of heart. Many, many things can go awry." LOL.