The 32-year-old tried to force through a move from the Baggies to Queens Park Rangers in January but failed, and eventually ended up in Cardiff in the summer.
"Of course I have regrets," he told The Mirror. "There was a time when I couldn't escape it and I shouldn't have done what I did in January. I still get the jokes and the banter even now from other players, but slowly it goes away.
"But I was a very good player for West Brom. My son was born the night after I scored an equaliser for West Brom against Aston Villa in January.
"I always gave everything. I believe, especially as I'm older now, that you owe it to yourself to fight and battle for your career, to do what's right for yourself and to keep your dreams and ambitions alive. I felt I had to leave West Brom to do that."
Odemwingie added that staying at West Brom for the second half of last season was "hard" but insists that he is now "happy" in Wales.
"After what happened in January, the next six months were hard and I came to Cardiff rusty because I didn't have a proper pre-season," said the Nigeria international. "But I knew in August that I was going to leave. I put in a notice of termination which expired on August 30. So, I was confident I would leave.
"It's the year that I will remember the most in my 10 years of playing. I've been through a lot and while it was all happening my baby son Noah was born.
"I'm happy now, I'm surrounded by happy people. I'm so motivated to help Cardiff stay in the Premier League."
Odemwingie joined West Brom from Lokomotiv Moscow in 2010.