The Hammers will spend the World Cup break just a point above the relegation zone after a third straight loss, 2-0 at home to Leicester.
Moyes has guided West Ham to consecutive top-seven finishes but this season has not gone to plan despite a £170million transfer splurge over the summer.
“Well, look, people are right because they’re not used to being in this position. They’re more used to being sixth or seventh in the league,” said Moyes.
“Last year, probably at this time, we were challenging for the Champions League, we’d been in the top four for long periods. So, I can understand that.
“I can understand, people want winning teams, want to be at the top of the league – so do we, so do the players. That’s what we’re planning to do next.”
Nine defeats in 15 matches this season represents West Ham’s worst start to a top-flight season since 1976 – and they have been relegated five times since then.
But Moyes added: “I thought the players worked unbelievably hard. I thought they ran a thousand miles trying to get a result.
“The lads were determined to try and make it work for us so it was certainly nothing to do with them not being quite at it.
“They’re low because they are desperate to win, they are low because they are a side who in the last couple of years are used to being sixth or seventh in the Premier League. They are not used to being in the position they are in, with the group we’ve got.
“I don’t think we are a huge distance away from it, but we’ve got to start showing it by the results.”
By contrast, Leicester’s fourth win in five Premier League matches means they have completely turned around their poor start to the season, when Brendan Rodgers’ side were being booed off and banners in the crowd were calling for action from the board.
Rodgers was cheered to the rafters as he applauded the away end at the London Stadium, and he said: “I didn’t see any banners! They must have been put in the shed the last couple of weeks.
“We can play home and away and we know we can score goals, but now there is a real resilience with the team. When you look at our clean-sheet record, over the last eight games, you see that.
“It is a huge testament to the club. The club have never wavered.”