"There is a feel-good factor here. Our job is to keep our feet on the ground but if the supporters want to dream they can," BBC Sport quotes Clarke as saying.
The former Chelsea coach went on to express his sympathies for Long, whose grandmother recently passed away.
"I know Shane Long's grandmother died and our thoughts go out to Shane who is going out to Ireland for the funeral," he added.
The result puts West Brom up to fourth place in the Premier League, one point behind Chelsea above them.