Earlier Isa Nacewa had given Leinster some much-needed breathing space with a try on the hour - but even the GUINNESS PRO12's meanest defence conceded late on as Josh Navidi touched down with two minutes to go but it proved too little too late for the Blues.
And Wilson insists Cardiff must learn from the narrow lose and quickly if they're to enjoy an improved run until the end of the season.
"We executed the game plan first half - we didn't in the second," admitted Wilson. "We've spoken about it in the dressing room just now because ultimately it is very frustrating.
"The conditions were difficult to play in, but second half it was our issue that was wrong and not the weather.
"There is nothing wrong with the effort, nothing wrong with the passion. We worked extremely hard and first half especially played some really good rugby. But it's another loss and we have got to take it on the chin and try bounce back from.
"Recently we've had a good run of wins and then for two games we've lost when we've been in a position to win," he added.
"One soft try was the difference between the teams. We got caught on the short side with no defender and it was a walk in really from the pressure we had.
"We've got to look at ourselves and learn a big lesson from this. First half we were good into the wind, but second half we were poor with it."
To buy tickets for the GUINNESS PRO12 Grand Final click here. Also follow us on Facebook, join the conversation on Twitter, sign up to our YouTube channel for extensive match highlights and sign up for our newsletter for regular updates on the GUINNESS PRO12.