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 insisted he was looking only as far ahead as Wednesday night's trip to Swansea.
He said: "I don't know. I don't know is the honest answer.
"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.
"Our focus is on Wednesday night, that's as far ahead as we look."
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.
Sunderland's fortunes took a further turn for the worse two minutes before the break when Mignolet fumbled Chris Brunt's harmless through-ball to hand Shane Long a second goal on a plate.
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 confidently converted a controversially-awarded 81st-minute spot-kick after Johnson was harshly 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.
Clarke could hardly have enjoyed a better start to his managerial career, but again, was refusing to be carried away.
He said: "I don't dream too much, I'm a realist. I knew the squad of players I was taking over was a good squad, I knew it was a squad comfortable in the Premier League.
"They had finished mid-table and mid-table with 47 points both seasons. We knew we had added some good players to the squad, and we were hopeful that we could have a good season.
"So far, we have done okay."
Sunderland boss Martin O'Neill, whose side have now won just two of their last 20 league games, was able to take some positives.
However, injuries to John O'Shea and Lee Cattermole - the defender has a calf strain and is likely to be out of action for several weeks, while the midfielder aggravated a knee problem - left the Northern Irishman with fresh problems ahead of Tuesday night's home clash with QPR.
He said: "I think there's a lot to take out of the match, a lot to take out of it. We have been beaten, but we look as if we can maybe get a goal again now, which is very encouraging.
"We have a big game on Tuesday night and we will try to get ourselves prepared for that."
O'Neill was quick to leap to Mignolet's defence after his rare error strengthened West Brom's grip on the game.
He said: "Simon has been fantastic for us, absolutely fantastic. He is entitled to something like that now and again.
"It's absolutely and utterly out of character. It just slipped out. He has been terrific for us."