Despite going ahead twice, first through Shane Long and then Gareth McAuley, Wigan pegged the home side back both times, thanks to a goal apiece from Arouna Kone and James McArthur.
Callum McManaman completed the comeback with ten minutes remaining, giving Wigan a crucial three points and leaving Clarke with just one win in six from his faltering squad.
"You could tell from the early stages of the game that Wigan were the team that had something really to play for," he told Sky Sports.
"Nobody can question our attitude or commitment or desire to win the game because it was clear for everybody to see that we were trying to do our best to get the three points.
"But sometimes at this stage of the season that little bit extra mental spark can make a difference. I think that probably helped Wigan get the three points today."
Despite the loss, West Brom are still well placed to attain their highest ever finish as they sit eighth and five points clear of Swansea with three games left to play.