A try in either half from Jonathan Sexton and a third from Andrew Trimble helped a clinical Ireland to the win, although visiting fans were put through a nervy final few minutes as the hosts piled on the pressure.
Damien Chouly went over for what he thought was the winning score in the right corner late on but the final pass was adjudged forward by referee Steve Walsh as Ireland held on for a famous victory.
The defeat leaves France finishing fourth in the table after a mixed campaign which saw them triumph over England on the opening weekend but go down 27-6 in Cardiff last month.
And while Saint-Andre accepted the late decision on the forward pass, he praised his side for their dominance of large chunks of the encounter.
"It was a forward pass, yes, but we don't know with this new rule whether if you pass behind if it's forward or not. It's like this - one day it will turn on our side," said the 46-year-old.
"The guys were criticised all week but we showed a lot of good things but to be honest sometimes it is better to win ugly rather than lose like this.
"I think our young team did very well. It's a shame in the run of the game if we had more of the control we should win.
"Congratulations to Ireland. They played very well and have done so all tournament so they deserved it."