Swansea continued their positive late-season form by drawing 2-2 at fifth-placed Norwich City on Saturday.
Williams, who took over at Swansea in early January, says he wants to emulate the Canaries in 2024-25 by mounting a play-off push.
This has been a traumatic campaign for Swansea, who for much of the season were looking nervously towards the relegation zone.
But they have climbed to 13th courtesy of an upturn in fortunes under Williams, claiming six wins and three draws in their last 12 matches.
The creditable draw at Norwich – who have not lost a home league fixture since 5 November means Swansea have taken 10 points from their last four games.
Yet Williams says the challenge for his improving team is to keep on progressing.
“We have to drill down into the performance and show them ‘this is what got you the success, so this is the bare minimum’, he said.
Then of course if you stand still you go backwards, so if we reach a level, we have to say OK, now more’. That’s unfortunately the life the players need to live – every time they reach a standard, they have to push beyond that next time.
They are showing they can do that so that’s the way we are going to continue.”
Swansea will aim to reach 60 points for the season – and extend their unbeaten run to five games – when they host Millwall on the final day of the campaign next Saturday.
