The Hammers capitulated to a humiliating defeat in Sunday's (11.02.24) London derby in the Premier League and Moyes was particularly irked by how badly his team defended.
The coach said: "A really poor day for us. Very difficult to explain how we played so poorly.
"Arsenal played exceptionally well, we must give them the credit.
"The disappointing thing for me is, since I’ve come back to the club, I don’t think my teams defend like that ever. The disappointing thing is we were weak today, didn’t do the jobs well enough, didn’t fight to contain harder. We could have conceded other goals as well."
Angry fans streamed out of the London Stadium at half-time with the team four goals down and Moyes understands their fury - although he highlighted that they have enjoyed lots of good moments during his time in charge.
The Hammers boss said: "To be a football supporter, there’s always going to be bad times. Especially this club, who people know a lot more about than me - I came back twice to keep them out of relegation.
"It was only three months ago when we were having probably the best time West Ham have ever had. Let’s be fair, probably the last three years have been as good a time as West Ham have had.
"I still think this club has grown, [but] undoubtedly we’ve had a terrible day today. So I understand them, totally, in leaving. Sometimes at football clubs you’re going to have bad days. Today we had a bad day. But I certainly won’t forget the good ones."