Leigh Halfpenny was coolness personified when he kicked a match-winning penalty in the last seconds which looked unlikely after Bradley Davies' sin binning and Tommy Bowe's subsequent try had given Ireland a 21-15 victory.
And Kidney lamented his side's decision to sit back and invite pressure after taking the lead.
"When you lose with the last kick of the game it is very disappointing," Kidney said.
"There was a bit of ebb and flow and we had put ourselves in a good position five minutes from the second half but Wales held the ball and made good ground on us.
"You can't defend for that long and hope to win it and we put ourselves under an awful lot of pressure by letting them have the ball for as long as they did."
Davies controversially only received a yellow card for a tip tackle on Donnacha Ryan that Irish supporters felt warranted a red card and Kidney bemoaned the current luck of the Irish.
"There are lots of things that happen in rugby matches. We have to hope that at some stage it will swing our way.
"The fixture list, with a six-day turn around, is going to be difficult. We'll take a look at the video, not practice too much on the pitch and make sure we're fresh for Saturday night (against France.)"