Reigning Grand Slam Champions Ireland scored two tries during Byrne's 10 minutes on the sidelines and the Ospreys star realises that his error proved costly.
"I'm gutted. I let the players down. I take responsibility," Byrne said in his column for the Independent on Sunday.
"The coaches have drummed into us the importance of keeping our discipline. I didn't. And I hold my hands up."
Byrne's sin-binning follows on from Alun Wyn Jones' yellow card during last month's loss to England - a lack of discipline that cost Wales 17 points in their 13-point reverse at Twickenham.
Byrne himself had no qualms in recognising that his own mistake proved equally detrimental at the weekend.
"Ireland scored 10 points when I was off the field," added Byrne.
"It was a key moment of the game. Yellow cards almost always are at this level.
"I don't need to be told how costly they can be, particularly after what happened at Twickenham.
"I know what I did wrong."
Wales were actually on the attack at Croke Park when Byrne received his marching orders, with critics suggesting that his offence was totally unnecessary.
The 29-year-old incensed South African referee Craig Joubert by knocking the ball out of the hands of Ireland scrum-half Tomas O'Leary after being caught in possession and turned over on the edge of the opposition 22.
And while Byrne doesn't agree entirely with Joubert's version of events, he readily admits that his mistake was a carless one at least.
"What happened? Well, I was in the bottom of a ruck in their 22 and on the wrong side.
"As they went to move the ball away I just caught it with my hand. It wasn't deliberate, but I'm not going to quibble.
"The referee had just issued us a warning. I shouldn't have been there.
"I'm told my expression of disgust as I walked off was on television. I apologise if anyone saw it and was offended.
"What can I say? I was just so annoyed with myself."