The two return as members of the Indians, and hit eighth and ninth, respectively, on Monday against Tampa Bay.
"I had a heckuva time playing with my great teammates last year, love them all," Kotchman, a native of St. Petersburg, said. "What we were able to do was historic and great to be a part of."
Damon, who grew up in Orlando, also said that his time with the Rays was special, albeit short-lived. When he does retire, though, he said he plans to make the trip to Tropicana Field to watch the Rays play.
Both players said that because of family, friends and community connections, it was difficult to leave the Rays, but reaffirmed that they're happy with the Indians.
Damon, who hit .261 in 2011 with the Rays, said he originally expected to be back this season, but saw the chances slim when Tampa Bay signed Luke Scott.
"With everything that was said on the final days and during the offseason, hanging out with the players, I think everybody expected me to be back," Damon said.
"You have to change uniforms sometimes. Sometimes it's your choice, sometimes it's not. You always have to make the best out of every situation," he added.