And with both England and France both recording comfortable final weekend wins, Wales slipped to fourth.
"Finishing fourth is another kick in the groin, but that's the way it goes," said Williams.
"We will learn from this season. We haven't become a bad side over the last couple of months - we've played some good rugby at times - although consistently, we haven't played for 80 minutes in all games.
"There were a lot of turnovers in all our games and a lot of mistakes, but we are not a bad side, and hopefully we can work on the things that didn't go right.
"It is very difficult to win every game in this tournament. You are playing against the best teams in Europe, and I think Ireland have been the form side.
"It's strange that after all the effort you end up in fourth, but that's the 6 Nations for you. We will take it on the chin.
"But it is great for the Irish boys that they can experience a Grand Slam. "We've been there, it's a great feeling, and they deserve it."