The Hammers are without a win in 2024 having drawn four and lost four of their eight games this year.
Their last three results have been particularly poor, with Manchester United, Arsenal and Nottingham Forest combined scoring 11 goals against them without reply.
Some travelling supporters held up banners in the away end at Forest that said ‘Moyes Out’ and the Scot addressed the protests in his post-match press conference.
“I don’t think you can ever please everybody but I think it’d be hard to say that there have been many better times at West Ham,” he said.
“Maybe they want something different but I think if they’re honest it’s probably been as good a time as they’ve had at the club regarding winning a trophy, the league positions.
“Maybe they’ve had managers who excite them more, but the one who’s sitting here wins more.”
Moyes added: “I’m really disappointed that we didn’t win today, I’m disappointed with the results, but you mustn’t forget the good results, you mustn’t forget the wins this season.
“We’re sitting in a strong league position, this time last year we were nearer the bottom. As I said it was only three years ago that we were a team fighting relegation so we’ve moved on a long way away from there.”
