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.
Belgian winger Roland Lamah's early opener for Swansea was cancelled out by a superb 25-year strike from Stephane Sessegnon in the 52nd minute.
The Baggies - who before the game were only clear of the bottom three on goal difference - then pushed on and Congolese midfielder Youssouf Mulumbu side-footed home the winner from outside the box on 85 minutes.
It was West Brom's first away win since they upset Manchester United at Old Trafford in September, but more importantly for Spaniard Mel, it was the first time he had tasted victory since taking charge on January 9.
West Brom are now three points clear of the drop, but the former Real Betis boss will not allow his charges to look any further forward than their clash with Hull City at the KC Stadium next week.
"The next match is the most important for us - the first - Hull City," he said.
"We need to win again. The most important thing now is to look at the next game, only the next game.
"Tomorrow I am pleasured, the players are happy, but only for tomorrow. The next training session it will be important to work hard, and get together again."