A 4-2 victory at Sunderland clinched a fourth successive Premier League win for the first time in the club's history and saw the Baggies leapfrog Chelsea as a result of the best start to a season in 59 years.
However, asked if they could replicate what former club Newcastle did last season and mount a sustained assault on the big guns, Clarke said: "I don't know is the honest answer."
He added: "All I know is up until now, we have done very well. We have had a lot of plaudits and the players deserve it because so far, we have been a really good team.
"But you don't get carried away in the Premier League. We are still this side of Christmas, there are a lot of games to be played, a lot of points to be fought for."
West Brom reached the break in complete control but without having out-played their hosts. They took the lead on the half-hour courtesy of a fine finish by Zoltan Gera, who took full advantage of Adam Johnson's failure to cut out Gareth McAuley's long ball to turn and smash a left-foot shot past Simon Mignolet.
The Baggies looked to be cruising to victory until Craig Gardner's 73rd-minute free-kick clipped fellow substitute Marc-Antoine Fortune in the defensive wall and flew past keeper Boaz Myhill, which prompted a late flurry. Substitute Romelu Lukaku converted a controversial 81st-minute spot-kick after Johnson was penalised for a challenge on Liam Ridgewell, and although Stephane Sessegnon pulled a goal back with three minutes remaining, Fortune cemented victory in the fifth minute of stoppage time.
Sunderland boss Martin O'Neill was quick to leap to Mignolet's defence after his rare error strengthened West Brom's grip on the game.
"Simon has been fantastic for us, absolutely fantastic. He is entitled to something like that now and again," he said. "It's absolutely and utterly out of character. It just slipped out. He has been terrific for us."