"To be given that award is pretty awesome," said the Canadian journeyman, who recorded nine goals and 25 points in 26 games.
"The emotions going through your mind when you look up and see your teammates give an ovation like that, it’s pretty special."
Kings coach Darryl Sutter said the award went to the right person.
"It's great for Willie," Sutter said. "You could see how emotional he was about it."
Team mate Marian Gaborik was equally happy for Williams.
"He was amazing," The right winger said. "This is his third Stanley Cup, and I’m very happy for him. He deserved it."
This season, the Kings' first three series all went to seven games with L.A. having to rally from behind to clinch in Game Seven in each of them.
"Getting that (Conn Smythe) trophy will never sink in for the rest of my life," the 32-year-old Williams said. "But what we went through for the Stanley Cup this year is the story. We really earned it this year."
Williams was drafted 28th in the 2000 NHL Draft by the Philadelphia Flyers. After four seasons and a slew of injuries, Philadelphia traded him to the Carolina Hurricanes in 2003.
Two seasons later, he scored the final goal in Game Seven of the Stanley Cup Finals against the Edmonton Oilers. Following more injuries in Carolina, the Hurricanes dealt Williams to the Kings, where he’s been an essential cog to the team’s success, including a previous Stanley Cup trophy in 2012.
During the 2012 postseason, Williams scored 15 points.
In 2004, Williams was a member of Team Canada when they won the 2004 World Championships in Prague as well as the 2007 Moscow side.
(Reporting by Will Robinson; editing by Amlan Chakraborty)