Defeat meant the Ospreys missed out on a mouth-watering semi-final with Munster in Wales, with the Irish giants instead travelling to San Sebastien for their last-four clash next month.
But despite his own disappointment at falling just short in Europe once more, Williams was upbeat in his assessment of Munster's chances of reaching a fifth Heineken Cup Final.
"Munster will have watched our game closely and they will realise Biarritz are beatable," said Williams, who toured alongside the likes of Paul O'Connell, Donncha O'Callaghan, John Hayes and Ronan O'Gara when the Lions visited New Zealand five years ago, before also being joined by Keith Earls and David Wallace in South Africa last summer.
"Anything can happen in the Heineken Cup but we have shown that you can score tries against Biarritz.
"We all know what kind of team Munster are and they will have to take their chances.
"They can't afford to give away penalties or concede possession to the likes of Yachvili and Damien Traille. They are top class players."
One of those players highlighted by Williams admits beating the Ospreys was a massive result for the 2006 Heineken Cup runners up.
Star scrum-half Dimitri Yachvili was at the centre of a last-minute controversy that left Ospreys fans feeling particularly aggrieved at the 29-28 defeat.
Yachvili went on to explain his actions, while at the same time sending Munster a warning that the Basque side will mean business on May 2.
"I was worried it might be a penalty but the ball just touched my hand," said Yachvili.
"The referee said, 'Knock-on but there's no time to play the scrum.'
"But I did the same in the first half and the referee didn't say knock-on when they scored their first try.
"Of course we can win the competition and we will give it our all.
"We are very proud to have beaten the Ospreys because they are a high-level team.
"We were the better side especially in the scrum and line-out but the Ospreys were better physically than us. They were fitter.
"We were very powerful and efficient but we will need to improve against Munster."