Alexander Kacaniklic netted the winner for Fulham after on-loan Chelsea striker Romelu Lukaku had cancelled out Dimitar Berbatov's opener as Albion slumped to their third home defeat of the campaign.
Clarke said: "It was a poor first half from us but a much better second half. On what we produced in the second half, we deserved at least a point out of the game.
"But the first half was really disappointing because we've set really high standards here at The Hawthorns and we didn't reach them in the first half.
"It is difficult, four games in 11 days, the physical and mental tiredness as well and I just asked the players to dig deep within themselves and find something.
"But having got back into the game, we switched off and allowed Fulham to steal a goal on the counter-attack which makes it doubly difficult because then you have to go and raise yourself again."