Tuesday's 2-1 home defeat at the hands of West Ham was West Brom's fourth in succession in the Premier League.
Albion took the lead at The Hawthorns through Craig Dawson's header, but goals from Kevin Nolan and James Tomkins saw them slip to 16th in the table, just a point above the bottom three.
Head coach Alan Irvine has come in for criticism from the fans in recent weeks - most notably in the 1-0 home defeat to Arsenal at the weekend - but Lescott says it is the players who must shoulder the blame.
"The manager tends to get the stick but the players need to realise what we're doing is not good enough, we're not picking up any points," he said.
"It's not great for anyone. They [the fans] can vent their frustration but they have to realise we want to win as well - just as much as them."
