The result moved the Baggies up to fourth position in the Premier League, just a single point behind the current European champions.
Clarke believes that his side can now think of qualification for continental competition, but conceded they must work hard to keep up their form:
“At the moment, we are in the right position to think about Europe – but we go from game to game.” He told SkySports.
“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.”
Since taking the hot-seat at the Hawthorns from Roy Hodgson, Clarke has instilled a more attacking philosophy.
The ex-Liverpool assistant is happy with the results of his style:
“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.”