Mohamed Salah and Fabio Carvalho had Liverpool 2-0 ahead before Kai Havertz's consolation as Arsenal lost their preseason friendly 2-1.
Arteta said: "We all have to start competing and earning our right to show how good we are. But the team’s looking good. With the games I’ve seen in preseason, it’s clear what he ‘s been trying to implement. It was a tough game for us.
"I think we are in a good condition. I think we played soem really competitive matches. Today was a really strong test. I think we started the game fantastically well. I think after 6 or 7 minutes it should be 2-0 up for us and then we lost control, especially for two things that we didn't do well enough.
"And we allowed them to run in transitions, which is a really dangerous thing to do against them. And the second half, we improved a lot. And we deserve more, I think, but it was great. Really difficult conditions to play, a great crowd and we got a lot out of it so I’m really pleased."
On Arsenal's youngsters, Arteta also said: "I'm really pleased with all of them. Unfortunately I wanted to give opportunities to all of them, we didn't have enough time to do so. But especially the ones that played, I think they performed and responded incredibly well.
"So that's something that we take from the tour as well, that we have a lot of talent there that we want to use and they showed that they are very much pushing to earn the right to play with us."