England's slip cordon spilled a number of chances while New Zealand's close fielders were almost flawless in their work around the bat.
“New Zealand's catching was excellent, ours was disappointing,” Farbrace told reporters.
“We can't have to keep creating 13 or 14 chances every innings. We're going to learn from every series, learn very quickly and rectify some of the mistakes we've made over the last five days.”
England captain Alastair Cook agreed.
“We took some wonderful slip catches against India last year. We'll have to do some serious work before Australia as we know they make such a big impact on games,” he said.
Joe Root and Mark Wood were guilty of dropping catches in the series but the worst culprits were Ian Bell and Gary Ballance, who also endured disappointing struggles with the bat.
Bell made only 43 runs in two tests and appeared to have a serious problem with judging balls outside his off stump while Ballance, who contributed 36 runs, was clean bowled three times by the New Zealand pace attack.
Cook, however, played down the worries over England's numbers three and four.
“If everyone's in form, you'd score 800,” Cook said. “Ballance and Bell have had tough series, but they're wonderful players, it's not so long since they were scoring hundreds in West Indies.
“I have no concerns about those two. You don't score 1 000 runs in your first year as a test player (Ballance) or 7 500 test runs (Bell) without being a great player.”
Cook was happy to have rediscovered some form with knocks of 162, 75 and 56 ahead of the Ashes series.
“It has been a challenge against their bowling attack but I'm pleased to score some runs,” said the opener who became England's highest test run-scorer during the second test.
“You need to judge well outside off and I've managed to do that which is nice. Our batting has looked good. We could have batted out the day today but those four early wickets hurt us.”
Original source: Farbrace laments England butter fingers