Ah, so you're drawing directly into the (J)Applet?
the JApplet class only extends the awt interfaces, so it doesn't have many features.
Also, putting everything in panels gives you the option of moving those panels to another frame, giving you the possibility to escape from the (usually way to small) browser window.
So, yeah, I'd say using one or more panels for the different UI items is a good idea
By the way, I really like the fact that you can combine gems from your picks with ones on your board before picking a gem from picks!