But rather than write off his side's chances of claiming just a second tournament title in 27 years, Kidney remains hopeful that his side can bounce back, starting with a win over France this Saturday.
"Three teams have had their Grand Slams ended this weekend and three teams are still in it. That is the nature of it, but there is a championship still to be won," said Kidney.
"There are different aspects of the game I know we can improve on. It's just a case now of getting ready for the next match in six days' time."
Controversy surrounded the enthralling encounter in Dublin as Wales lock Bradley Davies and Ireland flanker Stephen Ferris saw yellow for separate tip tackles.
And while Davies was deemed lucky to escape with just a 10-minute spell in the bin, Irish fans claimed Ferris' hit on Ian Evans - which handed Halfpenny the chance to land the winning penalty - should never have been penalised at all.
But even though emotions were been running high following the last-gasp reverse, Kidney refused to blame referee Wayne Barnes and instead chose to focus on Ireland's areas of weakness as they go in search of just their second success in Paris since 1972.
"We'll take a good look at what we can solve ourselves first…and let the powers that be look at everything else," added Kidney.
"We've buckets to work on. I know we are a lot better than that.
"We put ourselves under a lot of pressure defensively. We had to defend for 60 per cent-plus of the game and, if you do that, you are going to ask for trouble.
"You have to give credit to Wales as well. Sometimes it is not just all down to you, but there are some aspects that we can be disappointed with individually.
"I couldn't give the lads more credit for their attitude, though. They work extremely hard, and their professionalism I wouldn't question for a minute."