Zola's fate is still unclear, however, with speculation continuing that he will be replaced.
"A lot of people say he is a nice man but he is not just a nice man, he is an extremely talented and good manager," Parker told West Ham's website.
"People will say I would support him but, from the bottom of my heart, he is a good man and he is a very good manager, along with the staff he has got here. Hopefully we can go and push on next year."
He added: "I don't think I would have had the season like I have had personally without him behind me.
"He has given me massive belief and confidence and, from my reaction, you can see that I respect him."