The Baggies right back believes the club's end-of-season form will not be influenced by the deadline day events surrounding the Nigerian striker's failed move to QPR.
Odemwingie, who was subject to two unsuccessful bids from Queens Park Rangers in January, arrived at Loftus Road on transfer deadline day in an attempt to push through a last-minute deal, despite the Baggies saying that no agreement between the two clubs had been reached.
As a result, Odemwingie's actions were blasted as "wholly unprofessional" by club chairman Jeremy Peace, and the striker was told last Friday not to return to training until this week, as well as being left out of the squad that lost 1-0 to Tottenham on Sunday.
"We'll deal with it," Reid told BBC West Midlands. "We've got a lot of strong characters in the dressing room. Peter's with us from now until the end of the season and we've got to deal with it as a squad."
West Brom's defeat to Spurs means that the Baggies now sit in ninth place after going six league games without a win, and Reid says he will be frustrated if they slip any further down the table.
"After the start we had it would be disappointing to let it fizzle out to midtable or lower," Reid said. "We've got a great points tally on the board, so it would be nice to kick on now and finish the season with a bit of a flourish."