Kindey's side, who have now failed to beat New Zealand in their previous 23 outings, were outscored by nine tries to four at the Yarrow Stadium, with All Black fly-half Dan Carter pulling the strings.
But Kidney was keen not to overreact to the indiscipline shown by his side and backed his players to put this set-back behind them and come back stronger against a New Zealand Maori outfit on Friday.
"It was a horror show. We gave away a lot of soft tries and missed a lot of tackles. We'll have to have a long hard look at that," said Kidney.
"We have to look closely at the discipline. I wouldn't want to say anything now. We will take a good look when we calm down a bit from this defeat.
"They picked themselves up at half-time, you saw that and we managed to keep the ball a little better in the second half."
Ireland face the New Zealand Maoris on June 18 and finish their tour down under with a test against Australia in Brisbane on June 26.