Arteta's penalty was the most meagre consolation after the Gunners had been blown away by four goals in the first 20 minutes at Anfield.
Martin Skrtel's brace was added to by Raheem Sterling and Daniel Sturridge, with Sterling later adding Liverpool's fifth goal.
With Arsenal facing Manchester United on Wednesday before an FA Cup rematch with Liverpool, Arteta told national newspapers: "We have to react.
"We know we need to improve and face those games in a different manner because after 18 minutes we were 4-0 down and it was like a car crash.
"The manager was really upset at half-time because it wasn't good enough for this football club. It was the angriest I have seen him."
Meanwhile, reserve goalkeeper Lukasz Fabianski has turned down the offer of a new contract at the Emirates Stadium and will leave the club in the summer in the hope of boosting his international prospects.
Fabianski has won 21 caps for Poland but has been largely frozen out at Arsenal, serving as back-up to international colleague Wojciech Szczesny.
"I want to be number one in the club and in the Polish national team," Fabianski said in comments reported by the Daily Star.
"I have learned a lot at London during very positive and challenging periods.
"With biggest respect to this great club, I didn't accept the extension offer as I am looking forward to a new challenge in England or abroad."