With about 10 minutes left to play, Ireland were driving towards the Welsh line and looked set to cross over for a try that would have given them the chance to retake the lead.
However, Barnes ruled Ireland centre Robbie Henshaw had joined a maul in front of the ball carrier and blew for a penalty, dashing the visitors hopes of a comeback.
Englishman Barnes had been a major factor in Ireland's defeat on their last visit to Wales two years ago when he repeatedly penalised them at the breakdown for tacklers not rolling away.
Ireland coach Schmidt said Barnes had made the right call at the Principality Stadium on Friday.
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"Wayne Barnes was on the spot, you can't join the maul in front of the ball," he said. "Did it have a material effect? I don't know. I think we would have scored anyway.
"It was tough. We scored 10 points in the 10 minutes we were down to 14 men and that's hard to come back from.
"We had good pressure on, there were a number of things we have to be better at. It's incredibly frustrating. Credit to Wales. When they are under pressure they come up with big moments." Much was made of Barnes’ appointment before the game and the fact Ireland have lost six of nine previous Six Nations matches under his control.
Ireland skipper Rory Best said his side were to blame for the loss, not the referee.
"We felt we were mauling well but Wayne Barnes is a top referee and that is one error we made which we are most disappointed with,” he added.
(Reporting by Mark Gleeson, editing by Peter Rutherford)
