Arsenal had little going forward as Declan Rice's first goal for the Hammers secured the east Londoners' first home win over the Gunners since 2006.
Chelsea's win over Newcastle meant the gap to the Champions League spots for fifth place Arsenal is now six points, while Manchester United moved level with Emery's side with a win at Tottenham on Sunday.
“Now it’s more difficult, it’s clear," the Arsenal boss said of their top four hopes.
In Pictures | West Ham vs Arsenal | 12/01/2019
"I think the most important thing for us is to recover our confidence and be more competitive. We need consistency over 38 matches. Now it isn’t enough at the moment. Saturday was a bad result."
The result meant Arsenal are now without an away League win since November, losing to Southampton, Liverpool and West Ham during that run.
Emery, who will now begin preparations to close the gap to Chelsea when they visit the Emirates next weekend, has called on his side to show more confidence when on the road.
“It’s our challenge. Each match is our challenge away. We are working on that," he said.
"It’s also the opposition team. Like here, for example, they are with their supporters, they feel good and strong and can push. We need to take more confidence, more performance collectively, being competitive away to change this moment.
"We started the season away well, being competitive and winning. And then sometimes we are doing but we need to do more to be more competitive and to impose our idea and our quality. West Ham also have very big players.”
Emery, who revealed he had told Mesut Ozil that he would not play a role at London Stadium the night before the game, said the German remained a good player in his eyes but that the trip to West Ham may not have been for him.
“For me he is like another player," Emery said of the midfielder.
"It’s one decision, when is coming one player or not coming. Sometimes he is helping us, at other moments not helping us because of his injury or because maybe the match is not for him. But he is a good player.”
