Although Ireland made it three bonus point wins from three and boast a plus-81 points difference that shows their dominance, Farrell said his side would be "licking their wounds a little bit" watching the remaining weekend action.
He was critical of his team's passiveness in attack in the first half and failure to take advantage of their dominance in the scrum, but praised the huge impact of his forward-heavy pack in earning the bonus-point late on.
"I suppose the bottom line is we got there in the end by being really tenacious and tough. We wanted to be better today but the opposition always has a say in that and Wales certainly did today," Farrell said.
"We've a bit of fixing to do and hopefully we can get better for Twickenham."
While Ireland are victories over England and Scotland away from a second successive championship clean sweep, Wales face the prospect of a potential final day wooden spoon decider against Italy, should they fail to upset France.
Coach Warren Gatland said his inexperienced team could take a huge amount from the performance, likening it to his time as a player with Waikato in New Zealand when they suffered big losses to Auckland before turning the tables on their rivals.
"I can't question the effort of the players and just how hard they worked," Gatland told a news conference, saying the scoreline reflected the greater experience of the Irish side.
"We've said all along that it's about the development of this team. It's making sure that we keep working as hard as we've been doing, keep getting better. It's all about the learnings for us."
