The 35-year-old quarterback was in attendance at the Town and Country Hotel in Mission Valley to honor former Chargers teammate Nick Hardwick, who was being inducted into the Breitbard Hall of Fame.
"It really was special over the last decade," Rivers said in a nearly four-minute speech at the 71st annual Salute to the Champions event. "The only regret I have is not winning it all while we were here. It's something we always wanted to do and get done for this community and for our team."
"It has been very special to be a San Diego Charger," Rivers continued. "And I hope that you can always see me as that.
"I know it'll be different, but just know that ... I'll play like crazy and fight like crazy, as a Los Angeles Charger, just like I did for you guys. And I know y'all can respect and understand that. But I hope you also know that I will always be playing for San Diego as well."
Rivers concluded his speech by saying that, having grown up in Alabama, he never would have hand-picked San Diego as an NFL destination, joking, "I didn't really know where it was on the map."
"But I am surely forever grateful that I've been able to spend 13 years here and call it home," he said in closing.
According to the San Diego Union-Tribune, Rivers said he took into account the team's potential move to Los Angeles when he decided in 2015 to sign a contract extension through 2019.
"My time here and my love for San Diego will always be great," Rivers told reporters Tuesday night. "I'll be forever grateful for my time there. But at the same time, I hope the people understand here, too, that I do have to move forward and get excited about where we're headed."
Rivers shared with reporters an anecdote involving his son Gunner and their unofficial tour of the Chargers' new home, the StubHub Center.
In town for a LA Clippers game this winter, Rivers and Gunner made a stop in Carson to check out the 30,000-seat venue that will host Chargers home games for the next two seasons.
Despite the stadium being locked, they managed to get inside and have a look around.
"It was like I was at an old high school stadium," Rivers told reporters in explaining his thinking. "Maybe one of the gates is unlocked, and we can take a peek."