Hibs go into this weekend's fixtures in fourth place and will seek to bounce back from successive losses to Inverness and Motherwell with victory at Kilmarnock on Sunday.
Following the Rugby Park fixture, Hibs face Ross County on Boxing Day, Celtic and then Hearts on January 3 before a two-week hiatus.
Williams said: "It's a point in the season now with so many games coming thick and fast, you can either make up a lot of ground in the league or you can drop. We really need to make sure we're making up ground.
"We've got four games now in quick succession. It's important that we pick up a decent amount of points, even if it's a case of trying to keep hold of Celtic, hold on to their coat tails before the winter break."
Hibs could fall out of the top four for the first time since October 1, depending on the result at Pittodrie tomorrow between Aberdeen and St Johnstone, while eighth-placed Killie and ninth-placed Hearts are only five points adrift.
Williams recognises the need for Pat Fenlon's men to reverse recent results to achieve the end-of-season goal of a top-six place.
"It's incredibly tight," said Williams, who has impressed since signing a two-year deal after leaving Colchester in the summer.
"You can win two or three games on the bounce and you can move up from sixth to second and people are asking questions of whether you can catch Celtic, whether you can win the league.
"You lose and you're talking about relegation. It's still very early in the season. It's important we manage expectation and stick to the focus we had at the start of the season, which was a top-six finish."