The Hammers raced into a three-goal lead and The Owls looked to be dead and burried.
But what looked like a sensational fightback thanks to goals from Graham Coughlan and David Graham came to an end when David Bellion hit the winner.
Sturrock said afterwards: "Even though the result is a negative, there are still plenty of positives - not so long ago if we had been 3-0 down then we would have capitulated and lost by four, five or six.
"But we rolled our sleeves up, fought hard and gave a good account of ourselves at the end."
In other news, sacked striker Adam Proudlock hopes to resurect his career at Ipswich Town after he repordetly was offered a trial.