The Kiwis needed 32 runs for victory off the last 18 balls in Sunday's match in Melbourne, but the game swung sharply when Brendon McCullum and Hamish Marshall plundered 22 runs off the third-last over, bowled by Kasprowicz.
New Zealand went on to win the opening match by four wickets with two balls to spare.
Chief selector Trevor Hohns said nothing should be read into Kasprowicz's absence from Wednesday's second game against the Kiwis and he expected the big Queenslander to return for the final One-dayer in Brisbane on Friday.
"The plan was to give him a blow (rest) at this stage come what may," Hohns said. "There's nothing to be read into him missing Sydney."
"Kasprowicz has been an outstanding performer over the last 12 months and he went for a few runs in one over in a One-day game and that can happen to anybody at anytime," Hohns said.
The selectors had rested fellow Test fast bowlers Glenn McGrath and Jason Gillespie from Sunday's One-day International.