Speaking before Swansea return to action on Saturday – against West Brom, coincidentally – Williams said he could “totally understand” fans’ frustration over his comments.
“I’m very, very happy to be here and I couldn’t think of anything worse than walking away from this place,” he added.
“So I apologise to anyone that felt I was showing a lack of commitment. I think my blasé approach was more that I just felt it was ridiculous that anyone would even suggest it.
“I have not even been here one year. We have just secured Ben Cabango [on a long-term contract], Liam Cullen is playing out of his skin and is in the national team, Joe Allen came out of retirement and is in the national team. I think we have the most perfect fit as a captain for any football club.
“I am glad that it (the West Brom link) is over and now we can try to make Swansea the best it can possibly be. That’s what I came here to do.”
Williams will celebrate a year in charge of Swansea on Sunday.
His side go into the weekend in 12th in the Championship, six points outside the play-off places, having made clear progress since Williams took over midway through the traumatic 2023-24 campaign.
Williams’ Swansea deal runs until 2027 and the former Notts County boss says he would “love to see the contract out as a bare minimum”.
“I feel like I’m just about getting started,” he added.
“I’m not going to walk out after the starter. The main course is coming.
“I have still got a lot to prove to the Swansea fans and I am going to set about doing that.”