Jason Alexander arrives at the 27th Annual Casting Society of America Artios Awards held at the Beverly Hilton on September 26, 2011 in Beverly Hills, California. Credit: Ryan Miller/Getty Images

Jason Alexander didn't understand why his "gay game" joke was offensive at first, but he does now -- and he's sorry.

The former Seinfeld actor appeared Friday on CBS' Late Late Show with Craig Ferguson and talked about the game of cricket.

"Have you ever played cricket?" Craig Ferguson asked. "Cricket's an amazing game."

"It's a gay game," Alexander, 52, said. "There's a lot of people wearing white. People wearing helmets for no discernible reason…Everybody breaks for tea in the middle."

Ferguson joked, "Yea, it's a cross between baseball and Downton Abbey."

But on Sunday, Alexander wrote a lengthy apology on Twitter that he said was "a message of amends." The star said shortly after his appearance, "A few of my Twitter followers made me aware that they were both gay and offended by the joke. And truthfully, I could not understand why."

But after spending some time thinking about it, Alexander says he realizes he was wrong. "And the worst part is – I should know better," he wrote. "My daily life is filled with gay men and women, both socially and professionally. I am profoundly aware of the challenges these friends of mine face and I have openly advocated on their behalf."

"So, I can only apologize and I do. In comedy, timing is everything. And when a group of people are still fighting so hard for understanding, acceptance, dignity and essential rights – the time for some kinds of laughs has not yet come. I hope my realization brings some comfort."