A 1-0 loss at Chelsea on Boxing Day followed a defeat to Everton and means Swansea have one win in six Barclays Premier League matches and 10 points from the last 10 games.
The 11th-placed Swans are just four points better off than 18th-placed Fulham, who occupy the final place in the relegation zone, entering their second match in 48 hours against a Villa side beaten at home by Crystal Palace on Thursday. Villa, who are one point behind Swansea in 13th, have lost their last four games.
"We have lost the last two, so it's going to be a massive game for both teams," defender Williams said on swanseacity.net.
"It's very important. Every game is in this league.
"They lost to Palace at home on Boxing Day, and they will be desperate to make up for that particularly as they are at home again.
"Villa Park is a very tough place to play but we know we are capable of winning there and bouncing back from these back-to-back defeats."
Williams is adamant Swansea are not unduly worried by their position in a tight table.
"There is no concern for us with the defeats and the gap between the teams below us in the table," he added.
"Our aim is to put some distance between ourselves and the teams below us. We don't want to get caught up in that because there aren't any teams that are really falling away. It's very close."
Swansea boss Michael Laudrup will make changes for the trip to Birmingham.
Striker Michu, midfielder Nathan Dyer (both ankle) and goalkeeper Michel Vorm (knee) missed the Boxing Day loss at Chelsea, along with defender Garry Monk (knee).
Leon Britton returned from a broken toe and could continue.
The midfielder recalled the 2-0 win at Villa Park almost two years ago and called on Swansea to play with optimism.
"We have to go there and be confident," he said.
"We have won there in the past so we know what it takes to win there."
With two games in such close proximity, Laudrup made his selection for Stamford Bridge with the second game in mind, but not tailored for Villa.
The Swans made six changes at Chelsea and a similar number could be made as they bid for a first win since the defeat of Newcastle on December 4.
Laudrup said: "Of course it had an influence. Not because it was Villa, but because it's two games in 48 hours.
"I had to make some choices. We have a couple of players with four yellow cards, people coming back from injury. There were a lot of things to take into consideration.
"I had to pick a competitive side. It was a little like a puzzle. Keep the number of players that have to play two times 90 minutes, or 90 and 70, down to a very minimum."