A Ben White own goal put the home side in front before strikes from Mohammed Kudus and Jarrod Bowen early in the second period put the tie beyond doubt.
Arteta left out Declan Rice on his return to the London Stadium, with the England international alongside Bukayo Saka, Martin Odegaard and William Saliba on a star-studded Arsenal bench.
Aaron Ramsdale was handed a rare start since he was dropped in favour of David Raya, but it was a night to forget for the Arsenal goalkeeper. White beat Ramsdale to Bowen's dangerous in-swinging corner but could only head into his own net after 16 minutes.
Eddie Nketiah did start for the visitors, fresh from his first Premier League hat-trick in a 5-0 demolition of Sheffield United on Saturday. But he missed Arsenal's best chance to get back on level terms when he blazed over just before half-time.
November 1, 2023
Instead, Kudus made it 2-0 on 50 minutes with a brilliant touch and low finish from Nayef Aguerd's long ball forward. Rice was then introduced to a mixed response from the West Ham faithful.
But any hope of an Arsenal fightback was quashed by Bowen's strike from the edge of the box on the hour mark. Ramsdale should have done better to keep out it out despite a slight deflection off Jakub Kiwior.
Arteta threw on Saka, Odegaard and Gabriel Martinelli in the closing stages and it was Odegaard who grabbed a consolation deep into stoppage time. However, it was too little, too late as Arsenal's 30-year wait to win the League Cup goes on.
November 1, 2023