Charlton won the game thanks to a brace from Dennis Rommedahl and sole strikes from Matt Holland and Darren Bent but despite Wednesday's resistance, Paul Heckingbottom's double was not enough.
Athletic will now go on and play Leyton Orient at home but The Owls will have to concentrate on their survival in the championship than a money-spinning cup run.
Sturrock said: "They had five clear-cut chances, scored four and three of them were created by our side and backward passes. The fourth goal epitomised it.
"Offensively as a unit I was quite happy. But defensively I'm not because we've lost four goals at home."
Former Wednesday striker Jon Shaw was one of the stars as little Burton Albion shocked the mighty Manchester United as they held the Old Trafford club to a 0-0 draw.