A goal apiece from Shane Long and Peter Odemwingie grabbed victory for the Baggies and moved them to fourth in the league, three points clear of Everton and just five off top-of-the-table Manchester City.
Saturday's scalp, following hard-fought defeats of Liverpool and Everton earlier in the season, has prompted some to suggest that Champions League football may be heading to the Hawthorns in due course.
The former Chelsea assistant manager remains realistic, however, but admitted that it is an exciting time to be a part of the club.
"Can we think of the Champions League? I don't look that far ahead, I look from game to game," Clarke told reporters.
|BOINGING UP THE LEAGUE|
|6/1||West Brom are 6/1 with PaddyPower to secure a top-six place in the Premier League|
"It is a great time to be at the club and, if the supporters want to dream a bit, they can but, within the camp, we will keep our feet on the ground."
The Scot was also keen not to downplay his team's qualities after such a sterling performance, suggesting they can be a match for anyone.
"We are a good team and a good group. Anybody you put in can go in and do a good job for the team," he continued.
"We've shown this year we can challenge all the teams."