Williams, Mike Phillips and Jonathan Davies all touched down to hand Wales a 22-10 victory, dashing Irish hopes of reaching the last four of the tournament for the first time.
And the Welsh wing paid credit to the “fantastic” effort of his team-mates, who resisted relentless Irish pressure to seal an historic victory.
â€œIt was a massive performance, we knew they had a lot of big ball carriers and there was a lot of tackling stopping them on the gain line because they are dangerous, it was a fantastic defensive effort,â€ Williams said
â€œWe always say we donâ€™t start good enough, and we started perfectly today and it was just what we wanted. Itâ€™s easier to be ahead of the game than chasing it. Itâ€™s a massive achievement and we have worked so hard.
â€œThe team in 1987 did it [reached the last four] and got third place. But we have the semi next week, the boys are thrilled and itâ€™s a massive achievement, itâ€™s brilliant.â€
Meanwhile, Ireland captain Brian Oâ€™Driscoll admitted their opponents were just too good and rued his sideâ€™s inability to recreate their memorable performance against Australia in the group stages.
â€œWe got outplayed in the second half, they scored two good tries, maybe there was some weak defence but we are very disappointed to be going home,â€ Oâ€™Driscoll said.
â€œIt was a great opportunity after winning the group but they proved worthy semi-finalists and good luck to them.
â€œWe needed to deliver a performance similar to against Australia or Italy last week, but we didnâ€™t, we knocked on too much ball and when you turn too much ball over against quality of opposition they make you pay and we are the ones left disappointed.â€
MORE: The latest football news
MORE: The latest tennis news