The Gunners romped to a 6-0 victory on Sunday - their biggest away win in the Premier League - as they reminded Liverpool and Manchester City that they intend to play a big role in the title race.
It was sweet revenge for the 2-0 home defeat by West Ham in December and a League Cup loss to David Moyes' team in November.
"Time to beat West Ham; we all knew it," Arteta said when asked about the mood in the squad before the game.
"We all had it in our tummies and we knew it would be a tough match and we had to do certain things better in both boxes than we had in the previous match. We certainly did today."
Last week's defeat of leaders Liverpool put Arsenal back in the thick of the title race but a trip to West Ham looked awkward on paper given recent experiences.
But Arsenal were sensational, with Bukayo Saka scoring twice and Declan Rice scoring and having two assists against his old club as the north London side moved back to within two points of Liverpool and level on points with champions City.
Saka missed a penalty last season against West Ham as Arsenal were held to a 2-2 draw, having led 2-0. It was one of a series of results that scuppered Arsenal's title hopes.
This time, Saka converted from the spot to put his team 2-0 ahead after being taken down by West Ham keeper Alphonse Areola.
It was his 50th goal for Arsenal, making him the youngest player to reach that landmark for the club since 1978.
"He's proving everybody wrong that he can do it. I had doubts whether he was going to take the penalty or not because of what happened but it shows you as well how mature he is and how determined he is to go to the next level," Arteta said.
"And today what he's done with the penalty as well shows that he wants to learn from a situation and make it right and that shows a lot of personality."
Saka said his teammates had "smelt blood" at West Ham and had gone for the kill.
Arteta added: "What I smell is a team that wants to be better and better. The way they trained this week they are totally focused after Liverpool, saying now it's a big test and now we have to go to another level to beat West Ham."
Check out the match report from the London Stadium with Flashscore.
