Odemwingie was the centre of a bizarre incident on transfer deadline day after driving to Loftus Road on Thursday in a bid to force through a move to QPR.
However, Albion quickly released a statement saying Odemwingie was there without permission and QPR revealed they had refused him entry to their ground.
Albion chairman Jeremy Peace accused the Nigeria international, who still has 18 months on his contract at The Hawthorns, of acting "wholly unprofessionally".
Odemwingie on Friday admitted he was perhaps a "little unprofessional" but defended himself by claming the circumstances were not so different to when he joined West Brom from Lokomotiv Moscow in 2010.
He also put Thursday down to a misunderstanding.
"I came to this club (West Brom) in a wholly unprofessional way. I wasn't given any written permission by Lokomotiv Moscow but I arrived at this club. I did a medical, I don't think everything went so professional when I arrived," he told Sky Sports News on Friday.
Clarifying his comments, he said: "I'm saying that these things don't matter so much when adults are dealing with each other.
"I think there was a misunderstanding somewhere because I could have held my goodbyes to the (West Brom) players if I was told it is not going to happen."
Odemwingie felt he had been given the go-ahead from West Brom to complete his move to QPR, but conceded he did not have written permission.
He said: "They (West Brom) didn't give me written permission, but you know we are in England and when you're gentlemen you understand each other so easily.
"In my opinion, everything was done right and at the last moment, I don't know what really happened, but I think other people can answer this question as well.
"We were almost there, the club were angry that I went there and it was on TV. They weren't angry that I went there, but when it came up on TV that's when they said that this deal is off and why did I do that.
"So I understand the club to be honest, it was a bit unprofessional but we all know our positions and we were almost there."
Asked if he felt West Brom technical director Dan Ashworth had given him the impression the move was fine, the 31-year-old said: "I can say yes. Anyway, we have to find a way forward that's suitable for everyone now.
"The truth is we all went wrong somewhere.
"The last day yesterday we found an agreement, and the only question from what I understood from the conversation was a player they wanted from QPR and the question was who was going pay his wages."
Odemwingie is unsure what his immediate future at West Brom holds for him, but believes he is still likely to leave in the summer.
He said: "I love the club, I love the fans, I did perform here, I did enjoy myself here. I will always love the club, no matter what's happened, but I will still leave, it's just a matter of time.
"I'm not saying it in a harsh way. I mean my contract is going to run out in a year and a half, I wasn't offered an extension here.
"What I mean is my career as a whole will end one day, so will my contract here at West Brom. We're not enemies, it's all about football at the end of the day, it's nothing personal.
"There's nothing maybe illegal from any side, but maybe things went wrong, maybe a bit unprofessional, but with that we almost still got there."
On what might happen now regarding his West Brom career, he added: "I believe if West Brom brought me back here they think there is a way out in which I can be back on the pitch and give my best to the team."
Speaking outside the club's training ground, Odemwingie said: "I've had a chat with Dan Ashworth this morning [Friday] and the club will say more later.
"I have been given a few days off and will be back in training next week."
QPR manager Harry Redknapp said he felt sorry for the situation Odemwingie found himself in.
"I wasn't at all disappointed yesterday as I felt we made some fantastic signings," Redknapp said. "I was just disappointed the way the Peter Odemwingie situation went. I was disappointed for the boy.
"The whole thing was a bit of a mess. I felt genuinely sorry for him. I think there was a mistake. He travelled down and I think he thought the deal was done and that is why he turned up.
"I think he thought 'I better get down, have the medical, sign the forms' - it was just a mistake.
"It is now difficult as he has to go back to West Brom and get on with his life.
"It wasn't easy. He is not a bad lad, he is a nice, nice boy and that is what disturbed me last night, that he got himself into that situation and there was nothing sort of malicious in it.
"I don't think the deal would have been problem, it is just a player (Junior Hoilett) was going to go on loan the other way and decided he didn't want to go.
"The kid ended up turning up at QPR and it didn't happen."