Moyes said it was "too soon" for him to commit for next season after the Black Cats’ relegation was confirmed following a 1-0 loss at home to Bournemouth on Saturday and Hull’s 0-0 draw at Southampton.
Moyes, who took over the reins at Sunderland last summer, has been the subject of fan protests calling for him to resign.
"I think it's a question for two or three weeks' time," said Moyes. "I think we all need to reflect and look at everything from top to bottom."
The relegation is Moyes’ first as a manager.
"I feel for the supporters because they're the people who pay their hard-earned cash to come and watch and we've not given them enough this season," said the former Everton and Manchester United boss.
"I've had 400-odd games in the Premier League and I've got an idea of what a good squad looks like.
"My feeling at the start of the season was it was going to be a hard graft, and I'd rather be up front with people than tell them something different."