Clarke was unaware of an alleged bust-up between Odemwingie and right-back Steven Reid but believes his side are professional enough to deal with any tension in a positive manner.
Albion released a statement on Friday afternoon in which they confirmed the Nigerian international had been disciplined and had apologised for his recent actions.
The 31-year-old issued a series of Twitter rants against the club after a transfer request was rejected.
He then memorably turned up at Loftus Road without permission on transfer deadline day only to be left in the cold as his planned move to QPR collapsed.
Clarke said: "I don't think you can say everything is back to normal because what happened, the whole episode, is something that didn't need to happen.
"(But) I'm really pleased the club have come out with this statement because it gives me the chance as a head coach to move on.
"That's what myself and the players need to do. We need to move on and concentrate on the football. I think it is important you try and keep your squad together. That's what I've tried to do."
But Clarke admitted there may be some issues to resolve over time.
"It is difficult to comment on whether there is any hostility between individual members of the squad. They are in a different dressing room from me," he said. "Will Odemwingie's return have a destabilising effect? No it won't. I'm convinced of that.
"I couldn't deal with the matter until now. There was no resolution. Now there is a resolution we can move forward as a group of players. That is important."
He added: "I'm sure some of them will be happy the matter is resolved. In fact I'm hoping most, if not all of them, are happy the matter has been resolved and we can move on as a group of players.
"How people take it personally is between Peter and the other people. The most important thing is that professionally we move on as a group of players."
When asked to confirm if there had been a row between Reid and Odemwingie, Clarke said: "I don't know. If there has been a row between Steven and Peter, I'm sure it was an honest row.
"My biggest grievance on that one is if you are telling me someone in this building is letting stories out to the press, that's more upsetting for me than Peter and Steven having an exchange of words."
Clarke is still to decide whether Odemwingie will be part of the squad for Wednesday's trip to Liverpool.
He said: "That is still to be determined. I only got that statement half an hour before you guys so it's something we have to look at over the next two or three days. I'll involve him when I feel it is right to involve him."
Albion released the statement ahead of Clarke's weekly press conference at the club's training ground.
It read: "West Brom have taken disciplinary action against striker Peter Odemwingie in respect of his conduct over the past fortnight.
"Odemwingie has accepted his punishment. He will now resume full training with his team-mates and is available for first team selection."
Odemwingie said: "I understand how my actions have been viewed and I want to apologise to the club and our supporters for any distress I have caused.
"I want to reassure everyone at the club and our fans that I will continue to give my all whenever I am selected.
"We have enjoyed a good season so far and I aim to play my part in keeping the club as high up the table as possible."
Albion chairman Jeremy Peace said: "This has been an extremely difficult time for the club and it was imperative that we dealt with such a serious matter both fully and correctly.
"We made our position very clear throughout - both privately to Peter and publicly.
"Peter has apologised for his conduct to me personally and the club and our supporters as a whole.
"He has accepted his punishment and promised to comply with all club regulations moving forward.
"It was important that we resolved this episode as expediently as possible to enable everyone to focus on the most important issue at this club - competing in the Premier League."
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