Redknapp branded Foy's handling of the situation as "awful", but Clarke thinks the referee was right to let the goal stand. "I didn't think it was a foul," Clarke said. "I was confused.
"I just saw the ball go up and then in the net. I've seen it on the video and I don't think he has done a lot wrong.
"I didn't think it was much of a foul to be honest.
"That's why he's there and that's why we pay him all that money."
Djibril Cisse scored 22 minutes from time, but Rangers could not find a second to equalise Green's own goal and West Brom's opener, which came courtesy of a 30-yard drive from Chris Brunt.
Given that the result leaves QPR six points adrift of safety having played one more game than 17th place Southampton, Redknapp was furious at seeing a potentially vital point slip through his fingers.
"It was a blatant foul," he said. "I hate hearing managers moan about decisions and getting robbed. I don't do that or slag referees off or moan about decisions.
"Once a year I might have the hump with a referee. I never knock on their door but that today was poor, two vital decisions that would be so important to us went against us."
Redknapp, whose team now face Liverpool on Sunday, was also unhappy that Foy did not award QPR a penalty in injury-time when Stephane Mbia's header struck Liam Ridgewell's arm in the West Brom box.
"I think they were awful decisions. I think the ref got it completely wrong," Redknapp added.