The defeat keeps Ireland's painful run of never progressing past the World Cup quarter-finals in tact while Wales reached the last four for the first time since 1987.
And Bowe, who was part of the Ireland team that finished as runners-up during this year's RBS 6 Nations, was left to rue what might have been in New Zealand.
"Having topped our group and beaten Australia, we were confident coming in the match but we failed to do ourselves justice a bit and this will go down as a great opportunity missed," said Bowe.
"We had the chance to get into the semi-finals for the first time in our history and there will be a lot of people who were disappointed we didn't.
"Wales came at us in the first ten minutes with an intensity that caught us on the hop and their defence was superb. We were camped on their line but just couldn't get over the whitewash.
"We coughed up the ball a few times when we were under pressure but we had them under the cosh at certain stages but we didn't get the scores we needed.
"You could see them building in spirit from that. We suffered from tryline fever and rushed things a bit. I'm absolutely gutted."