Williams' second half goal helped the Swans to a comeback win at the Emirates - a win that moved them six points clear of the drop zone.
The Gunners started the better of the two and hit the woodwork a number of times in the game, but the Swansea captain felt his side deserved the win after their brilliant efforts.
Captain fantastic 'proud' of his players
Speaking to the club's official website, Williams revealed that he was simply thrilled with the performance of his team at a very tough ground.
A handful of changes were made to the line-up in order to keep the legs fresh, but the Swans worked brilliantly as a unit to inspire each other to come from a goal down to take all three points.
Williams will take the headlines but, whilst he was "obviously very happy to score the goal," he says that "the most important thing" was that Swansea "showed a great attitude" to get the result.
"I'm so proud of the guys," the captain said - and it's easy to see why, with them having taken three points from a losing position against "a very good team who are trying to win the league."
Swansea were second best at the beginning of the game and Arsenal did have "a lot of chances," but Williams believes the away side "showed a lot of character and determination" and really "deserved something from the game" in the end.
Time to build
Whilst the result in North London was certainly a huge one for the Swans, their captain is focused on not getting carried away and on keeping grounded ahead of the next match.
Though it feels great to prove people wrong, as "there were a lot of people that didn't think [Swansea] would get anything from the game," the South Wales outfit need to "back this win up" with another this coming weekend.
Norwich City are the visitors at the Liberty Stadium on Saturday, and Williams says that if his side don't win that game, then the Arsenal victory will mean "nothing."