"We were disappointed with how we started but good sides get themselves back into the game and we did that and possibly should have come away with a win," Wales coach Warren Gatland said.
"We dominated the territory and possession to get in front.
"Then to not execute an exit play accurately enough was disappointing. I don't want to take anything away from Ireland. They contributed well and maybe a draw was a fair reflection of the game."
Linebreaks were infrequent although Ireland managed to push Simon Zebo and Sexton into some holes while Wales rarely got their battering approach to breach. Wing George North managed a few forays and replacement starting fullback Liam Williams also looked handy.
Ireland's lineout was a steady combination between skipper Rory Best and his targets and their new looseforward combination bristled throughout the match. Their pack was unsettled in the scrums though as newer Welsh props Rob Evans and Samson Lee generated some frontrow heat.
"It's a better result than a draw normally would be," said the Ireland coach, Joe Schmidt. "I thought there were some really outstanding Welsh performances, and it will give us confidence that we managed to hang in there."
Ireland travel to Paris for their second round match this weekend while Wales host Scotland in Cardiff.