The Midlands outfit have slipped to 15th in the Premier League standings following a five-match winless run, including three defeats in the space of eight days.
A 2-1 loss at Newcastle United was followed by a 3-2 reverse to title hopefuls Manchester City, before a disappointing 2-0 home defeat to Norwich City on Saturday.
With just three victories in the top flight this season, West Brom find themselves just two points above the relegation zone.
But Clarke believes his side can climb away from danger through hard work.
Speaking to the Birmingham Mail, he said: "We had a bad week. Until last week the season been going okay. Sometimes that happens - but now it's a test of character.
"We need to stand up. I have no problems with the pressures - it's what I'm paid to do.
"Everyone says nice things about you when you're winning. And when you're not winning people are less kind and that's part of the job.
"I'm not a great believer in luck. If you work hard enough you get your rewards.
"It was a tough week for us and I did say we could suffer for the points we didn't pick up (earlier in the season), so we need to get through this period as quick as we can.
"Everyone has to work hard, I have to work harder, the players have to work harder and we try to find a solution as quick we can."
