Swindon midfielder Williams filmed the famous video of Wales players celebrating England's Euro 2016 exit to minnows Iceland.
The video was subsequently leaked on social media, sparking outrage among many England fans that another home nation should celebrate them being knocked out of a major tournament.
Williams said: "I was just the cameraman to be fair. I was videoing it and put it in the WhatsApp group.
"It ended up getting leaked and the manager (Chris Coleman) wasn't too bothered so I was alright.
"A lot of things went in that group chat that trip, but the only thing was there was a lot of players in that chat that weren't in the squad at the time.
"I think it was every Wales player that had played the last few years and I didn't know that.
"It was the summer and people were on holiday and it got leaked.
"We never found out who leaked it, but I get blamed anyway. There is much more tighter security now."
Wales had already booked their quarter-final spot at Euro 2016 when Williams filmed those celebrations of England losing at the round of 16 stage.
Six years on and Wales are in a far tighter spot at a major tournament, having picked up just one point from their opening two games at the World Cup in Qatar.
Wales must beat England on Tuesday - something they have not achieved since 1984 - and hope Iran and the United States draw their final group game to reach the knockout stages.
An unrealistic four-goal win over England would also see Wales through to the round of 16.
Despite dropping down to League Two, Williams is now at his third major tournament having featured at Euro 2016 - where Wales went on to reach the semi-finals - and Euro 2020.
Asked if he would film Wales' victory celebrations if they got through to the knockout stages, Williams said: "I don't think I will be the only one.
"There is extra motivation to win those games because they are rivals.
"We know what the England game means to the fans and we were so devastated when we lost to them in the Euros.
"There is no reason why we can't win, we have strong belief in every game.
"We have to as a nation, you have to have belief in yourself otherwise there is no point going out on the pitch."