The Baggies are lying in seventh spot in the table despite losing at home to Fulham on New Year's Day, with a 15-point gap between them and the relegation zone.
In contrast, Rangers are battling to survive in the top flight and are still five points adrift of safety.
Clarke said: "The FA Cup is a competition we want to try and do well in. I've enjoyed success as a player and a coach in the FA Cup and I'd like to continue in the same vein.
"We are only involved in three competitions, we went out of the League Cup early, but we'd like to stay in the FA Cup as long as possible.
"I assume QPR's priority will be staying in the Premier League and they had a great result at Chelsea which means they will be a bit more buoyant tomorrow.
"We are a little more comfortable in the league and are sitting in a reasonable position, one we want to try and improve on in the second half of the season.
"But the FA Cup is a competition we want to do well in."