The Baggies, on course for their highest ever Premier League finish, twice had the lead against the relegation threatened Latics.
But Roberto Martinez's men twice fought back to level the game before Callum McManaman's close-range strike 10 minutes from time gave the visitors all three points.
"You could tell from the early stages of the game that Wigan were the team that had something really to play for," Clarke 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."