The Hammers beat 10-man Aston Villa 4-1 to follow up their Carabao Cup win over Manchester City.
Hammers boss Moyes saw his team defeat London rivals Tottenham last weekend and reach the quarter-finals of the Carabao Cup with a penalty shoot-out victory against Manchester City before a 4-1 rout of 10-man Villa took the Hammers within two points of second-placed Liverpool and level with City.
Moyes said: “It’s been a great week. But you know what happens in football, it can quickly turn around and bite you.
“But I think we’ve got to the stage where we’re really confident in a lot of the things we do. The players are understanding their roles and what’s expected of them.
“We can’t let up, though, I’ve told them that if we think we’re doing great and it’s all easy it’ll fail, so we’ve got to keep at it.
“I’m really pleased with the result. The run we are on at the moment, it is really pleasing, coming to Villa and scoring four is never easy. This was a really tough game as they have a really good team.”
Asked about the raised expectations following last season, when West Ham finished sixth in the Premier League, and the strong start to the current campaign, Moyes said: “I think football managers have to try to raise the bar.
“After 10 games is a pretty good time to judge where you are in the season. The players are doing a remarkable job but none of us must think that we’ve done it as there’s still such a long way to go.”
Villa fell behind early on to Ben Johnson’s strike. Ollie Watkins equalised but Declan Rice quickly restored the Hammers’ lead before half-time.
Ezri Konsa’s red card shortly after the break gave Villa an uphill task and further goals from Pablo Fornals and Jarrod Bowen inside the final 10 minutes settled the contest.
The red card was a mess defensively for Dean Smith’s side. Kortney Hause caught Pablo Fornals in the face on the run before Konsa was initially booked for knocking Bowen to the ground right on the edge of the box.
VAR took a look at both incidents and decided that Hause had no case to answer, while Konsa saw his yellow card upgraded to red after referee Chris Kavanagh checked the monitor.
Smith disagreed with the decision, saying: “It’s a frustrating day and when things are going against you things happen.
“I don’t think it’s a red card. The referee has made his decision – yellow card. Is it a clear and obvious error? No, I don’t think it is.
“He’s not clean through on goal but when I spoke to the referee after the game he said (Bowen’s) touch has taken him towards goal. I’ve seen the replay and it’s not going towards goal so it’s a poor decision.”
Captain Tyrone Mings was the high-profile casualty of Villa’s change of shape to 4-3-3 following three successive defeats, with Konsa keeping his place.
Smith said: “It’s a big call whenever you select a team. We went to a back four and they are good at set-pieces and Hause is very good at them and Tyrone (Mings) has probably not been playing at the top of his game.
“I had to make footballing decisions and I made them. Some players weren’t available as well. Danny Ings and Douglas Luiz have soft tissue injuries while we also had some Covid-related issues.”
A fourth straight loss leaves Villa just three points above the relegation zone but Smith said: “I saw a lot of character from my team today and I am certainly sure we can turn it around with the squad we’ve got. There are reasons why we’ve had the results we’ve had.”