After the bitter disappointments of losing two Heineken Cup finals and last season's Celtic League final, the Williams' Munster side rose to the occasion magnificently to keep the trophy in Ireland.
'There is a definite sense of relief in the camp at finally winning a trophy. It's something this group of players wanted to do and it is good to come back and win the Celtic League after losing in last year's final,' said Williams.
'It has been a very difficult month for the side, but the supporters have been with us all the way. They follow us everywhere and they are an intergral part of the side.'
There were around 10,000 Munster fans among the 30,076 crowd at the Millennium Stadium and they entered into some joyous celebrations with the team at the end of the game.
And while the skipper was wearing a huge grin, the coach Alan Gaffney, who helped mastermind Leinster's victory over Munster last year, claimed it was a triumph for the whole squad.
'We have won this title as a squad and not as a team. We brought 27 players with us to Cardiff and there were around 10 players playing club rugby back home who have figured in the Celtic League programme this season.
'It has been a great performance all round. To lose only one game in 10 in the competition is a very good record.
'We knew we needed to get off to a good start and we did just that. We spent a lot of time in the first-half without the ball, but our defence was very good.
'At half-time we were 22-6 ahead and we made a pact that we weren't going to defend our lead, we were going to attack it. I think we suprised them a bit when we spread the ball wide straight away in the second half.
'Neath are a side that like to attack and, just as happened in our earlier game at The Gnoll, a lot of their attacking didn't translate into points. We took our chances well, but I don't think the scoreline reflected th nature of the game.'
Back row man Alan Quinlan took the man of the match award for his outstanding performance and it was his breakaway try in the first-half that broke Neath's back and hoisted his side into a 19-6 lead.
'I'm thrilled with the win. It's great to finally win something and get a piece of silverware,' he said.'It has been a massive effort from everyone.'
Ronan O'Gara was sent for an x-ray on his injured left ankle, although Gaffney said he wasn't too worried about the circumstances in which the injury occured in the first-half.
Former Wales flanker Brett Sinkinson was pinpointed by television for stamping on O'Gara at a ruck and forcing him to leave the game after kicking four penalties.
'Ronan is walking quite comofortably. We will have a look at it but I doubt we will do anything. I would have great diffciulty with that,' said Gaffney.
'Neath could proably look at a number of incidents the other way. We will always try to protect our players.'