"I'm sure they [the fans] appreciate that I gave everything for the club and I've got very fond memories," Griffin told BBC Radio Stoke.
"I've enjoyed every single minute of my time with Stoke City," added Simonsen.
"Whether it was playing a run of 100-odd games in the team without a break or whether it was being involved on the bench, I'm so proud to have been part of the phenomenal rise of Stoke City over the past few years."
Both players ended last season on loan at the clubs that they would go on to join for the 2010/11 campaign.
Griffin and Simonsen were key members within the squad that helped the Potters seal their return to the top-flight of English football for the first time in 23 years in May 2008.
"The promotion day was one of the proudest moments of my life," said Simonsen, 31.
"It was such a huge achievement for the city of Stoke-on-Trent and it will live in my memory forever."
Griffin's last Premier League appearance came in a defeat at West Ham in December 2008, in which he was involved in an on-field altercation with team-mate Ricardo Fuller.
The former Newcastle defender said: "It ended a little bit sour unfortunately, but I'm a Stoke City fan and my boy will support Stoke as well.
"I came through the ranks under Lou Macari [during the mid-1990s] and to come back to the club and captain the side to promotion was just a dream.
"I'll choose to dwell on the fond memories rather than the things that have happened recently. Hopefully Stoke will become a Premier League force for years to come."
Source: BBC Sport
Source: BBC Sport