While Millwall's players were celebrating a goal which was not given, The Owls raced down the other end to score after taking a free kick for one of the most controversial moments in the club's recent history.
Frankie Simek's first goal for the club was booed and jeered by the home fans in what they saw as a shocking refereeing decision.
Lee Bullen had to play the entire second half in goal after David Lucas was carried off with a season-threatening knee injury but The Owls were resilient to win the three points.
Sturrock said: "There have been times earlier in the season when certain things have not gone our way so we'll take the good with the bad. I can definitely see why Millwall are aggrieved but I'm not going to complain about that.
"I said to the boys at half-time that all the pressure was off them. If we won or drew they would be heroes and if we lost it would have been my fault."