Parker has no doubts this West Ham team are capable of much better.
Parker said: "It has been a horrible season, but we have put up with a lot of mess - only a few months ago we were reading this and that [about the club's future].
"I am not making excuses - at times we have not been good enough - but hopefully we have erased some of the bad things and we can look forward to kicking on next year, sticking together, learning from this and moving forward."
And on manager Gianfranco Zola, 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 [after the goal], you can see that I respect him."