Speaking ahead of Swansea's return to action on Saturday – against West Brom, coincidentally – Williams said he could “completely understand” fans' frustration with his comments.
He added: “I'm very happy to be here and I can't think of anything worse than being away from this place.”
“So I apologize to anyone who felt I was showing a lack of commitment. I think my vulgarity was more that I felt it was ridiculous for anyone to suggest that.
“I haven't been here for one year. We've just got Ben Kabango (on a long-term contract), Liam Cullen is playing out of his skin and is in the national team, Joe Allen has come out of retirement and is in the national team. I think we have the best qualities as captain of any football club.” .
He added, “I'm happy that (joining West Brom) is over and now we can try to make Swansea the best it can be. This is what I came here to do.”
Williams will celebrate one year in charge of Swansea on Sunday.
His side enter the weekend 12th in the Championship, six points off the qualifying places, having made clear progress since Williams took over midway through the agonizing 2023-24 season.
Williams' contract with Swansea runs until 2027 and the former Notts County boss says he “likes to see the contract as the minimum”.
“I feel like I'm about to start,” he added.
“I'm not going out after the start. The main course is coming.”
He added: “I still have a lot to prove to the Swansea fans and I will start doing so.”