The 28-year-old defender signed a four-and-a-half year contract after a £300,000 switch from Derby.
Griffin: "The Premiership is a very tough place to play in today, but I'm not shell-shocked.
"Before I got injured about four weeks ago I felt good and thought I was doing OK. Like anyone, I played some bad games and some good games.
"It's a challenge to go into the Premiership and it would be a big challenge for Stoke if, hopefully, we got promoted.
"It's a great place to be, but also not the be-all and end-all. That's why I am happy to come back to Stoke. If you find contentment in life then you've cracked it - and last year I found that here.
"I've got no desire to go and play for anyone else, so hopefully I'm here for the rest of my career.
"I will come in, keep my nose clean, work hard, have a bit of a giggle and talk to the younger lads to try and help them.
"If Tony sees me for something other than the football side of things, that's fine. Hopefully I will be a good servant."