After narrowly escaping relegation last season, the Hammers have surprised many in the ongoing campaign by sitting fifth in the Premier League standings at the moment.
They are just two points behind the Champions League spots and are expected to at least qualify for the Europe League, which would far exceed the expectations that they had at the start of the season.
The West Ham boss insisted that his team can only take one game at a time as they look to qualify for Europe and admits that it is going to get competitive towards the end of the season.
But he stressed even if they do not qualify for Europe, this season can be termed a success given what was expected of his side at the start.
Moyes said in a press conference: “I did say that when we get to single games I would look at it, but it is really tight and there are five or six teams who could certainly be in different positions.
“So what I have done in my head is simply take it one by one now and see where we go and then move on to the next one.
“But we were not expected to be in this position but we are going to try and do everything to stay in this position and if that get’s us into one of the European competitions then great.
“But if it doesn’t we will look at it and probably look and still see it as a good season so we will have to try and keep going and make it a great season if we can by making it into European competition.”
West Ham are next in action away at Wolves on Monday night and will be targeting three points.