West Brom have held several meetings regarding the Nigerian international and have sent him home for a few days after telling him he will not be involved in Sunday's game with Tottenham at the Hawthorns.
Odemwingie was fined two weeks wages, around £70,000, on Monday for breaking the club's social media regulations, following his tweets about the club rejecting a transfer request last weekend.
And it is understood Odemwingie will be facing another two-week fine for his attempts to force through a transfer to Queens Park Rangers yesterday, which has left Albion in an embarrassing situation.
Clarke has described Odemwingie's actions as "total lunacy" and admits it remains in doubt whether the player with 18-months left on his contract can repair the damage caused.
"Maybe he has to apologise. He has got to get back in the squad first and maybe he's got to get picked in the team. He has to show his team mates that he is ready to help them and if he is selected to play, he has to do well in games," said Clarke.
Clarke admitted that a deal with QPR could have been done yesterday and talks were on-going over the possibility of a £3.5 million sale and Junior Hoillett travelling in the opposite direction on loan, but the deal collapsed and Clarke re-iterated that Odemwingie did not have permission to talk to QPR.
"It has been unhelpful for the club. There was never a situation at any stage on deadline day that Peter was not our player. We were as surprised as anyone when he turned up at Loftus Road, because he did not have our permission," said Clarke.
"QPR know that and made it quite clear he did not have our permission, but this is not a case of having to get lawyers involved to sort things out. We will sort the matter out.
"We have already held a number of meetings about the situation. Peter has been in and he has been in meetings with Dan (Ashworth), Richard (Garlick) and myself and we are looking at the next part of the process.
"It is obvious there has been some form of misunderstanding on the part of Peter and his agent. Why would they turn up to Loftus Road without permission? There has been a misunderstanding on their part, but no misunderstanding on our part.
"West Bromwich Albion never gave permission and at boardroom level, there is absolute clarity. I have no idea why he went there. That is a question that needs to be put to Peter and his advisers.
"At some stage yesterday it was close to a deal being done, but lots of clubs try to do deals and they do not work out. I am sure a lot of other clubs were in the same position. It did not happen and fell through."
Meanwhile, QPR boss Harry Redknapp again insisted it was a simple case of miscommunication.
"He didn't set foot inside the ground - he just pulled up in his car, as you saw on TV. He definitely wasn't in the building. He stayed outside, but he made a mistake by coming down here - he shouldn't even have done that.
"I think he wanted to be around just in case the deal got done and he was on hand for the paperwork and a medical. He's probably driven down to London and thought, 'Where do I go now?' and he's headed for the ground.
"We played it by the book and West Brom have been fine about it - they are happy with the way we've dealt with it. The boy's just made a mistake - if you don't pitch up outside the ground, there's no problem, is there?
"It's a shame because he's a nice person, a good guy. I met him two years ago and he's a very educated boy, and he's not the first one who has found himself in a situation where things haven't worked out the way he wanted.
"He'll probably get some stick now - but a lot of people in football get stick, don't they?"