The Owls got off to the worst possible start when Steve Howard opened the scoring after only two minutes but Wednesday fought back to equalise through Graeme Lee.
David Graham scored his first league goal for Wednesday in the second half but missed a glaring opportunity just before half time.
Howard got Luton's second only a minute after The Owls had taken the lead but Sturrock was happy with his new signing's performance following the 2-2 draw.
He said: "I was pleased that we created lots of chances and I was also pleased David Graham got a goal but there was a good shape to us. David though was lively, he made good passes and linked things up for us."
But despite being happy with Graham's performance, Sturrock still wants his players to play more direct when the opportunity arises.
He added: "Some of our players are good players and they want to play football but there's times when we can't play football because we have to be dogged in our approach - we'll learn from that."