The Baggies, who sit two points above the relegation zone, have won only once in their last 10 league matches since beating Manchester United at Old Trafford in late September.
"There is no magic formula," Clarke told reporters. "There is no magic wand. It's difficult for the players and all we can do is keep trying as hard as we can to break the run as quickly as possible.
"I don't think it's lack of confidence. You can see the team plays with confidence - we try and pass the ball."
"You work as hard as you can, you hope you get a lucky break or you hope that someone does something fantastic," Clarke added. "One individual moment can change the run of games."
The only goal at Cardiff on Saturday came through Peter Whittingham's second half header, which was enough to put the hosts four points clear of the bottom three.
Last season's Championship winners hoped to capitalise on their decent home form, which has seen them beat Manchester City and Swansea City this season, and boss Malky Mackay was happy to get three points from a side so close to them in the table.
"It's another win and it's against a team that's round about us in the league as well," the Scot said. "It's an important win for us today. It's a good win for us playing against another proven Premier League team. We deserved to win in my opinion."
Cardiff's first league win since early November moved them up to 14th with 17 points with West Brom two places back on 15.