But like the rest of his team-mates, the Leinster full-back had mixed feelings when asked if the 17-17 scoreline was a good outcome.
"It is and it isn't," he said. "We still haven't won in Paris in so long. We came and we wanted to win.
"We knew we were good enough to win and we can't start taking this mindset that it was a good result, a good effort, the Irish fought hard again because we're coming second best and we're not going to be a competitive team that achieves if we take that attitude.
"So, I don't really buy that and I'd like to think that none of my teamm-mates do either."
The Louth man clearly felt Ireland should have closed things out after leading by 11 points at half-time. He highlighted the third quarter of the game as being a crucial period, when the visitors failed to come away with any points after spending plenty of time in the French 22.
"We're a good team. We have a lot of strong belief, we know what we can achieve, we know that on our day we can muscle up with some of the best teams in the world. And we did that," he explained.
"It's just that the margins are so small...I think we might have lacked that one or two percent of a killer instinct in us. These games are tiny margins and if we get another one percent of a killer instinct, we can close these games off."
Kearney will be hoping to demonstrate that cold-blooded attitude when Ireland take on Scotland at the Aviva Stadium this Saturday.
"I think it's about winning and having enormous self-belief as well," added the 25-year-old. "The more games you win, the more momentum you build and the more confidence you feel.
"If we have that inner desire and inner belief that we can beat anyone in the world, then we will. It all starts with mentality, I think."
Kearney's Leinster colleague Jamie Heaslip said the wet weather conditions in Paris made last Sunday's game a difficult one to play in.
"We felt very fresh, but it was a very stop-start game and to that degree a little bit frustrating because we didn't get to open up the game and play the brand of rugby we wanted to play.
"And they would probably say the same thing - they probably wanted to play that brand as well. I don't know if that's credit to both sides for their defensive efforts or what, but that's the way it went."
The Ireland number 8 is also looking forward to getting back to action as soon as possible.
"We're in good shape going forward. We've got Scotland on Saturday and a six-day turnaround, so we've just got to get our bodies right for that," he said.
"They are a good outfit - they are going well so we'll have to focus on them. That's all we can really do - we can only focus on the next game. We want to win and we want to end this Championship well."