Neal Maupay's first goal for the club earned a 1-0 victory over the Ironss at Goodison Park as the Toffees signed off for the international break in the best possible way.
West Ham remain stuck in the bottom three after another inadequate afternoon, which came on the back of Thursday's Europa Conference League trip to Denmark.
The Hammers have lost 13 of their 26 Premier League games in 2022 and Moyes knows his side have to rediscover their form.
"If you look back, we felt we were dropping down and we were aware of that and we were trying to improve it," he said.
"I recognised it probably February time that we weren't quite as strong. We chose not to bring anyone in in January and I could see it.
"But we got to a European semi-final, we were challenging until the last 20 minutes of the Premier League season to be sixth. We weren't dropping away that far, we were challenging but I just had a sense we were needing new players and a lot of those players played today.
"I need them, I need them to play at their best. I have seen the performances a lot of those players can put in. I am the one who takes the responsibility and I have got to get them back at that level quickly."