James Morrison and an own goal from Gary Caldwell put the Baggies in control before Arouna Kone reduced the deficit for the Latics. The midlands outfit are level on points with fourth-placed Everton, with only unlucky losses to Manchester City and Newcastle preventing them from soaring even higher.
But Clarke said: "I remember once as a player I was top of the league in November and ended up fighting relegation. The top division in England can come back quickly to bite you if you take your focus off it."
He added: "This week we're happy with where we are. I know it sounds boring, but we just have to keep working from game to game.
"Our away performances have been as good as our home performances so this is long overdue. I don't really see it is a monkey off our back but it is nice to end it sooner rather than later and especially at such a difficult place as Wigan.
"Even though our away performances have been good, we have had a habit of losing late goals and dropping points and you start to think about that, so it was nice to hang on and get the 2-1 win."
Clarke went on to single out stand-in keeper Boaz Myhill, who played his first senior game in 21 months in place of the injured Ben Foster, and could continue to deputise against Chelsea next weekend.
Clarke said: "To talk too much about Ben coming back would be disrespectful to Boaz. He has waited a long time for his chance and he came in and did well. His handling was excellent he had a really assured performance."
Wigan boss Roberto Martinez offered no excuses for his side's disappointing display, with Kone's close-range header moments after the Baggies' second goal the only bright spot on an otherwise below-par afternoon.
Martinez said: "I don't think we are the sort of side that can get a result out of a scrappy performance. I don't think we were as good as we could have been today, and that is really the frustration."