West Brom moved up to fourth in the Premier League after beating Chelsea 2-1 on Saturday and now sit just one point behind the reigning European champions.
Former Chelsea full-back Clarke is happy with the Baggies' form, but he is anxious not to get carried away by the club's best start to a Premier League season.
"At the moment, we are in the right position to think about Europe - but we go from game to game," said the West Brom boss. "That is boring I know, but I think this weekend we'll let the supporters dream a little bit.
"The team are certainly in a very good moment, but within the camp we'll keep our feet on the ground.
"I think people have been taking notice of us for quite a few weeks now. We are aware of that, they can take notice if they want, but we work from game to game."
Clarke has managed to make West Brom into more of an attacking threat since he succeeded the pragmatic Roy Hodgson who had made Albion hard to beat.
He said: "I wanted to try and make supporters go home happy at the weekend after watching a team who have played attractive football and tried to play football the right way and get positive results.
"We'll go chasing three points and, if we keep doing what we are doing, it can be a good season for us.
"We closed the gap on Chelsea and managed to put a few more points between some teams that are below us."