The Australian side were a goal up in four minutes after Ali Abbas ran clear of Mark Noble and passed to Corey Gameiro, who fired under Adrian.
A low shot from Alex Brosque doubled the lead on 26 minutes, and the 2-0 scoreline stood at the break as Aaron Cresswell missed the target following a one-two with Carlton Cole.
West Ham began the second half more promisingly and halved the arrears when a Matt Jarvis cross deflected in off defender Nikola Petkovic.
But the A-League side scored a third on 64 minutes through Gameiro, and the goal stood despite West Ham players appealing for handball by Terry Antonis in the build-up.
West Ham manager Sam Allardyce admitted his side had been poor, just three weeks before 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. It wasn't the best decision I've ever seen."
Skipper Kevin Nolan bemoaned the referee for missing a 'blatant' penalty and the controversial hand-ball of Sydney's third goal, but admits the fault is mainly at the door of the Hammers.
"The gaffer will have his word now and we’ll all be told," he said.
"Everyone knows, individually and collectively, that we’ve got a lot of work to do - but we’re ready and raring to go."
Matt Jarvis admitted the Hammers were disappointed to lose in front of thousands of fans from all over the world, and lamented their inability to turn chances created and possession into goals - the same issues that led to Wednesday's 2-1 defeat by Wellington Phoenix in Auckland.
"I thought we started the game well again in the opening minutes but then fell behind to an early goal, which was very disappointing," said Jarvis, who provided the assist for Mauro Zarate's midweek strike at Eden Park.
"We had a lot of the ball, but unfortunately couldn't get the ball in the back of the net as the first half went on.
"I'm enjoying it personally. I just need to keep working hard and getting fitter, stronger and sharper. I'm pleased with how it's gone as I've got two assists and two goals now."
West Ham are so far without a win in pre-season after a last-minute 2-2 draw at Stevenage, a 0-0 draw at Ipswich Town and losses against Wellington Phoenix and Sydney FC.
Their 2014/15 season kicks off on 16th August at home to Tottenham Hotspur.