The Baggies moved ahead of fourth-placed Chelsea with their 4-2 win over Sunderland on Saturday and remained there after the Blues failed to beat Manchester City on Sunday.
And Clarke has expressed his belief that there is no luck involved in the Hawthorns side's lofty position.
"It's certainly not been a lucky start," he told the club’s official website.
"We've earned every point we've got. You could even say we've been unlucky not to get more points in some games.
"It's been a solid start and we've deserved everything we've got.
"We're third and we deserve to be there. But we won't get carried away. We don't think that, because we're up there, we're big-time Charlies.
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Despite West Brom having taken 26 points already this season, Clarke says the main priority is still to reach 40 points to ensure survival.
"You've got to understand that safety is relative," he continued.
"The idea is you have to get 40 points. But I never said when we had to get those points. We’ve made good inroads towards that target. If we can get 40 points before the end of January, we can reassess things.
"But the first target is a sensible one and one we will try to deal with.
"We've seen a lot of clubs who have had a lot of points at this stage of the season and gone on to struggle come the end of the season.
"We hope we have the strength and depth in the squad for that not to happen but we will just keep building from game to game."