The Welsh side's home matches have followed a depressingly familiar pattern in recent weeks.
Against both Crystal Palace and West Brom on Saturday, the Swans dominated and hogged possession in the first half, went 1-0 up, only to produce a limp second period and allow their opposition back into the game.
Palace went away with a point, but the Baggies took all three to give their under-pressure head coach Pepe Mel his first win at the club.
Centre-back Williams played his 100th Premier League game for the Swans at the Liberty Stadium but was in no mood to celebrate having seen an expected win turn into a surprising 2-1 loss.
He said: "You might play bad, you might play good, but the effort level and the dedication to the game, and concentration, has to be 100 per cent in this league. You can play against any team and if you're not at it, you'll lose.
"I think (in the) second half we weren't at it for whatever reason and that can't, and will never, happen again."
Interim manager Garry Monk could not fathom why his side produced such a "sloppy" second half, having started strongly following a 13-day break after seven matches in 22 days.
Now sitting 14th in the table and four points above the relegation zone, Monk hopes his players will be able to show some of the battling qualities that sides "scrapping for their lives", like West Brom, are producing.