The Hammers finished two points behind fourth-placed Chelsea last season.
The Hammers finished two points behind fourth-placed Chelsea last season and Moyes wanted them to make up that gap this term.
As things stand they have done just that, lying in fourth and currently two points better off than they were at this stage last season.
“I think we’re in good shape,” said Moyes. “This was the time of year when we were coming into a good run of form in January, februar. It gave us a real chance to compete with the other teams.
“We want to hang on to their shirt tails and I hope we can keep it going. We’re in a good position going into the second half of the season.
“Last season we started to think about what we might be able to do but it was a bit later on, more kind of when we’d come out of the January schedule and we thought there might be a real chance. We challenged the players to build on it.
“So this season the challenge was laid down from the start. Can we pick up another couple of points which might be close to the Champions League?
“It might not be enough, but if we get anywhere near the points total last season we’ll have had a great season, so we’ll keep challenging, keep pushing. But we know we’ve got a really tough second half of the season to come.”
West Ham have come through the recent spate of Covid postponements relatively unscathed.
They had just one match, against Norwich called off due to the virus in the Canaries’ camp, and won the rearranged fixture 2-0 on Wednesday night.
While other clubs face a fixture pile-up, West Ham could have a far clearer schedule in the run-in which will surely benefit them.
“I hope so,” added Moyes. “Because we’ve had difficulties at our club, injuries and Covid, and we’ve had to continue playing. So I wasn’t pleased with where the Norwich fixture was put in.
“We’ve tried to be available for every game. So we would hope that it might make it difficult for those other clubs as it goes along.
“But we could easily fall into a batch of Covid and it could be us. I don’t think we’re over it yet, but I think we’re all hoping we might just be coming out of the end of the worst of it.”
Moyes also revealed that Manuel Lanzini has been called up to the provisional Argentina squad.
The midfielder is finally looking back to his best having suffered an ACL injury when he was on international duty prior to the 2018 Verdensmesterskap.