Defeat at Everton means West Ham have missed out on a place in the Europa League for next season.
Hammers boss Gianfranco Zola said: "The players are very disappointed.
"But I am even more disappointed we have not been able to make seventh place. But that does not taken anything anyway from our season.
"I am really pleased and proud to be their manager. Considering all the problems that were around the club, all the injuries we had, the players have done a fantastic job.
"I have promised them that next season we will be much better. I do believe that."