Norwich rejected three bids from the 27-year-old's old club Bournemouth during the transfer window.
"I'd like to apologise to the club and most importantly the Norwich fans for my actions," he said.
"Their support for me has been great since I joined and I really appreciate their passion for the club. The fans who travelled to Rotherham I especially apologise to.
"I've served a suspension and been fined, which I fully accept. Now I'm just determined to train hard and to let my football do the talking - and to do everything I can to help Norwich City do well."