Ronan O'Gara's late drop goal ensured another defeat for the Welsh, who themselves thought they had won the match through Stephen Jones' successful drop-goal attempt moments earlier.
Hansen said: "We performed just about as well as we could have but the history books will say they won the game.
"I am sure anyone who saw it will take it as the game it was."
Wales are heading for the wooden spoon unless they can pull off a huge upset and secure their first 6 Nations victory in France next weekend but Hansen is certainly not writing off their chances.
"The boys have to take confidence from the way they played against one of the best sides in the world," said Hansen.
"At the end of the game to dominate them physically from a fitness point of view is something you have to take a lot of heart from. We just have to start dealing with the Italys and Scotlands in this way."
The match did end in controversy, however, with Welsh fans expecting referee Steve Larder to award Wales a penalty when Ireland's Justin Bishop appeared to knock-on deliberately to disrupt a home move, but, after allowing the advantage, Larder let play go on.
Larder afterwards told the Welsh camp that his decision would have been a scrum for a knock-on and Hansen, to his credit, refused to complain.
"You've played for 85 minutes and you just have to take it on the chin," he said.
"It isn't worth talking about. I thought he refereed the game quite well and we have to move on. It isn't worth making an issue of."
He was also philosophical about O'Gara's last-ditch drop goal which secured victory for the Irish.
"All credit to Ireland it was fantastic for them to be able to come back and O'Gara had the composure to do the job.
"But we came back from that and threw the kitchen sink at them. It just wasn't to be. We performed as well as we could and 25-24 wasn't too bad."