Luis Suarez hit a hat-trick for hosts with Daniel Sturridge rounding off the goals, whilst James Morrison got the Baggies' consolation from the penalty spot.
Clarke said: "It was a difficult afternoon.
"We set up to be open in the game, but maybe we were too open.
"From 2-0 down it's always difficult to chase a game, and Liverpool are a good team.
"They've got good dynamic, their two front players are in form at the moment and we suffered at their hands."
Despite conceding two early goals, the Scotsman praised the effort from his team: "We kept going, so you can't fault the effort.
"We just gave ourselves too big a mountain to climb.
"To go 2-0 down after the first 20 minutes, it was difficult to get back in the game.
"I said to the players the third goal was crucial, and we conceded another one from a set-play which was disappointing.
"But we kept going, we kept working away. We created a number of chances in the second half, as did Liverpool, so it was an open game."