Your rings, trinkets, and accessories count for a large chunk of your stats. Getting them to at least exotic is very important for your combat effectiveness.

As has already been stated, you can just purchase exotic ones on the trading post for not a lot of gold. If you only need core stat sets for ascended there are some you can purchase with laurels. I believe there are some wvw and pvp methods of purchase as well.

You can check the wiki page on ascended gear for the various options and how to acquire them.

You might even skip the exotic tier for trinkets, because amulets, rings and accessories of ascended or even legendary quality (though most require Living World) are relatively easy to acquire. Not owning Living World pretty much locks you out of the more "fancy" stat combinations, but you can get ascended trinkets with Berserker and Celestial stats from Laurel vendors.

To add to the other comment, ascended also drop in fractals quite often and you can also buy them there.

Can recommend joining a guild that runs guild missions, since you can buy some in the hall for the currency you earn from those.

I would say that there’s no reason NOT to have exotic rings and trinkets. You can buy exotic gear on the trading post.

If you meant ascended, and not exotic, then I would say they are worth getting. Ascended gives about 10% in stats and you can buy some, if not all, with laurels?