Full-back Leigh Halfpenny landed a final-minute penalty to snatch victory in a nerve-jangling contest at Aviva Stadium.
Stephen Ferris emerged as the fall guy after he was harshly sin-binned by referee Wayne Barnes for a spear tackle on Ian Evans, offering Halfpenny his chance.
But Wales lock Bradley Davies was extremely lucky to have escaped a red card 15 minutes earlier for a far more dangerous example of the same offence.
Ireland's Six Nations resumes next Saturday in Paris where they have prevailed just once since 1972, but Kidney insists the title remains within their grasp.
"Three teams have had their Grand Slams ended this weekend and three teams are still in it," said the coach.
"That is the nature of it, but there is a championship still to be won.
"We will take a good look at what we can solve ourselves. There are different aspects of the game I know we can improve on.
"It is just a case now of getting ready for the next match in six days' time."
Lansdowne Road was treated to an engrossing final 15 minutes that appeared to be heading Ireland's way when slick passing sent Tommy Bowe over in the right corner.
But the imposing figure of George North, the most influential player on the pitch, proved the difference as he powered through three Irish backs to present Halfpenny with a tricky conversion to win.
The Lion missed on that occasion, but kept his nerve when it mattered most.
North had earlier battered his way through Ireland's midfield to set up one of Jonathan Davies' two tries and captain Paul O'Connell accepted the hosts had blown a good position when they led 21-15 12 minutes from time.
"We gave Wales a lot of ball earlier in the game that we shouldn't have done," O'Connell said.
"We put ourselves in a position to win the game but we conceded eight points in the last five minutes.
"We also conceded a lot of momentum in the first-half and gave them a lot of belief.
"We struggled to get into the game in the first half and you can't give a team that length of time with ball in hand.
"Defensively, we will have some work to do. We conceded a lot of ground and yardage at times, but when we attacked, we played with intensity."
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