The 32-year-old left The Hawthorns for Cardiff on deadline day following a dispute within the club that arose when he was denied a move to Queens Park Rangers in January.
"I have a lot to thank the club for, maybe not everything," Odemwingie said in a press conference. "Overall, we're both disappointed in how things ended up.
"To me, the fans are more important than the people who decide things in the club and I don't think we regret the three seasons that we had with each other.
"We're all human, we all make mistakes, and I believe that mistakes were made on the side of West Brom as well."
Odemwingie has also revealed that a number of clubs wanted to sign him in the summer.