Odemwingie, who was subject to two unsuccessful bids from QPR 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.
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|8/1||West Brom are 8/1 with BetVictor to beat Liverpool in their next Premier League fixture
Speaking to BBC West Midlands, Reid said: "We'll deal with it. 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 they 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 mid-table or lower," he continued.
"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."