Alex Pearce headed Reading level on the half-hour mark to cancel out Clyne's opener before Ambrose and Moses both scored in first-half stoppage time.
Substitute Gylfi Sigurdsson hit an 80th-minute penalty to briefly reduce the arrears before Moses cut in from the left to curl home a brilliant second goal.
Rodgers said: "We got what we deserved from the game which was nothing.
"We started poorly and then got worse. We conceded twice in first-half stoppage time which is incredible really and that totally threw us.
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Sporting Life