From Wickepedia....
As with the live action television series, the animated series was concluded before the resolution of the storyline, and we do not learn if the astronauts are able to return to their own time period. But the animated series does otherwise offer a conclusion. Doctor Zaius, in recognising the threat of a military overthrow from General Urko, assures that he is relieved of command. Further, Cornelius and Zira, in recognising that simian society was established long after human society had deteriorated, believed that the time was right for humans to be offered equal rights to that of apes and intend to present their proposition to the Senate.
Not exactly a satisfying ending though.
Having said that, I have to be honest and say that I have yet to do a proper marathon where I am actually concentrating on the animated show. My mind always wanders and I end completely losing the plot and giving up. I am determined to concentrate on the show right through one of these days! Not sure why it fails to grip me.