King insisted that the club had no intention of allowing Williams to leave last month, but have now had a change of heart to waive him from their roster.
The Nets will save cap space with the release of Williams, who is now expected to join the Dallas Mavericks on a two-year deal.
"I think we both made it work - tried to make it work - I think we had some great moments with him," King told reporters.
"I think we were being realistic and said, 'OK. We're not where we wanted to be, so now we reshuffle the deck, we have a great chance to create a lot of cap space for next year'.
"We're able to retain some young players. We kept some of the core together and added some new athleticism, so I think we're headed in that direction."
The 31-year-old averaged 13 points per game for the Nets last season.