Bowe and co were hoping to secure their first Grand Slam since 2009 but found an inspired Welsh defensive display too tough a nut to crack in Cardiff.
That means that Ireland's hopes of defending their title from last year will go into the final round of games with Wales, England and the men in green all having won three and lost one of their first four games.
And Bowe, who has made seven GUINNESS PRO12 appearances this season, insists he and his teammates can shake off the disappointment quickly enough.
"We'll be hurting now, we'll be disappointed 100 per cent in the changing room, the boys were very, very quiet in there with what we let slip," he told the Irish Independent.
"We'll come back into camp, we're straight back to Carton House, we've got it all to play for. The first opportunity for an Irish team to win back-to-back titles in I don't know how long.
"It's a massive match in Murrayfield next week and we'll be pumped up for it."
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