Speaking after West Ham's goalless draw with Manchester United on Thursday night, Moyes admitted that the job at hand was "tough" and that things "need to improve", though he did not state whether he would be around to spearhead said improvements.
"Of course we are satisfied to get a point against Manchester United," Moyes told Sky Sports News. "The attitude of the players was terrific. We were safe at the weekend but the players knew it was a big game, we wanted to move up the table.
"It's a big achievement for us [to stay up]. It has been a tough job but a really good job. We had to get the players in order a little bit after we came in, and we have done that. This is a big club and there are big expectations from the supporters so they will need to improve."
Asked whether his future lies at the club, Moyes replied: "We will have a chat next week and see how things go."
The Hammers wrap up their league programme with a home game against Everton on Sunday.