Andy Carroll thumped a header past Baggies goalkeeper Ben Foster to put the Hammers ahead and then powered home a well-taken volley after Gary O'Neil had made it 2-0.
The visitors' only consolation came through Graham Dorrans' penalty at the death while Youssouf Mulumbu saw red in the dying seconds for needlessly booting the ball at O'Neil.
Clarke said: "West Ham deserved to win. It was a difficult afternoon but we haven't had too many of those this season."
Clarke will speak to Mulumbu about his red card for petulantly kicking the ball at O'Neil in injury time.
He added: "I said to the group after the game that they must control their frustrations.
"It doesn't affect the game but it affects our group and our squad and the next three games. We have a small group and it's a big loss for us.
"He probably did it out of frustration."
- Sports & Recreation
- Youssouf Mulumbu
- Graham Dorrans