Former Carlton key forward Curnow was dangerous early at the MCG on Thursday night, kicking two first-quarter goals.
But he was blanketed by Tom Barrass after quarter-time, going without a kick and limited to just three handpasses as the Swans fell to a 14.15 (99) to 13.4 (82) defeat.
It came after Curnow kicked three goals in the season-opening win over the Blues and went goalless in a follow-up victory over Brisbane.
"The ability for Charlie to perform consistently, he's still working his way through at our football club," Cox said after his side's first loss of the season.
"One thing we try to say is, 'At all times, compete as hard as you possibly can and try to read the cues up the ground when we are bringing the ball through'.
"There's some inconsistencies throughout that at times and it will be a work in progress we've got to put time into."
Cox said Swans ruck star Brodie Grundy also has some adjustments to make, having given away another two free-kicks under new ruck rules introduced this season.
Grundy gifted the Hawks centre clearances by crossing the centre line before engaging his opponent, prompting a discussion with his coach at quarter-time.
"It was just about being decisive with your approach. Whatever you decide to go with, do it," Cox said.
"If you want to stay down you just can't cross the line. You know that, otherwise the timing adjustment you need to do.
"It's always learning and he gave away a couple last week, so it's just a different rule that they're trying to get used to. He fixed that, which was good."
Cox lamented Sydney's inability to win the ball at the coalface in the second half, when Hawthorn won a one-sided contest possession count 89-57.
But he refused to blame the loss on the absence of star duo Errol Gulden and Isaac Heeney, who went out of the team with injuries.
Heeney (hamstring) is a short-term prospect, though Gulden (shoulder) is expected to miss four months.
"At times you're going to miss your players that don't play," Cox said.
"But we went into the game extremely confident that the 23 that played could get the job done, and for parts of it they showed that."
Sydney have a 16-day break before their next game, when they take on Cox's former side West Coast in Perth.
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