The Gunners went down 3-1 at Anfield as Jurgen Klopp's side showed why they won the Premier League title last season.
"We were in the game for a big part of the game," Arteta said. "The reality is they are superior to us in many aspects. You could see that is some phases.
"I'm really happy in the way the team competed and kept believing. This is the standard we have to reach. We are on a different journey. They've been together five years, we've had a few months.
"They scored too early [after Arsenal's goal], big mistake from us. I had a feeling we were going to have chances in the second half.
"We had probably the best chance of the game. You have to put them in the net when you have chances against them.
"We have a long way to go in many things."