Demba Ba scored the only goal of the game in the 28th minute in a game of few clear-cut chances at Stamford Bridge.
"We thought we prepared well enough to get something from the game today but unfortunately we didn't," Clarke told the club's official website.
"We went to sleep on a set play and that's what cost us. We didn't create anything clear-cut but there were one or two scrambles at the end and you could feel the tension in the crowd."
West Brom are now ninth in the Premier League.