Arnold not carried away by Sydney win
Defeating Premier League oppositition is a rare feat but there were no exuberant celebrations from the Sky Blues boss at Wellington's Westpac Stadium.
"Of course it's great to win a game," Arnold said.
"But as I said when Wellington beat West Ham there are no points or trophy for it and it's the same for us.
"It's about us getting better and better every time we step on the pitch. It's about playing to the game plan and playing to the instructions."
Having lost 4-0 to Newcastle United earlier in the week, the Sky Blues fully deserved their victory against the Hammers and Corey Gameiro (two) and Alex Brosque deserved their goals.
While Gameiro was fortunate to be allowed his second – after Terry Antonis handled the ball in the build-up – his first inside the fourth minute was a great strike.
Brosque too showed good poise for his goal in the 26th minute.
Even when a cruel own-goal which deflected on off skipper Nikola Petkovic got West Ham back to 2-1 Sydney didn't panic and instead pressed hard in search of their third.
"Consistency is the key but if we can play like that every week (in the A-League) I'll be a very happy man," Arnold said. "I'm very proud of the way the boys have handled themselves."
It was West Ham's second successive defeat of the Football United Tour having gone down 2-1 to the Wellington Phoenix in midweek.
West Ham manager Sam Allardyce admitted his side had been poor, just three weeks out from the start of the Premier League.
"We've played two games and we've played poorly in them," said Allardyce.
"The football was not good enough to get results but we're experimenting and working on more open attacking play and it hasn't worked well from a defensive point of view."
The Hammers boss also felt the decision to allow Gameiro's second goal to stand had been "embarrassing".
"We would have been a bit more upset if we had been in a league match because it would have been a horrendous mistake," he said.
"It wasn't the best decision I've ever seen."
Hammers and New Zealand defender Winston Reid said the players had not been caught out by the standard of the A-League sides.
"I knew what to expect from the players who play in the New Zealand national team," Reid said. "A lot of them play in the A-League. They are not bad players at all.
"We came down here and we expected to do well and we didn't do so well.
"We'll go back home and work on some things."