Noone, a 68th-minute replacement for Jamie Mackie, struck late on after his tricky footwork fooled Isaac Osbourne out wide, allowing him to break into the area and coolly round goalkeeper Keiren Westwood.
He could have doubled his tally deep in injury time after Westwood joined Coventry's forwards for a corner but the 20-year-old's shot at an open goal from 20 yards went wide.
Sturrock spent the game sat down on the bench after surgery on an ingrown toenail, and from his viewpoint he could not see the goal.
"I didn't see Craig's goal because people were standing up in front of me but he did well to get into the box," he said.
"He can do that - but he also fouls four times straight after coming on and misses the open goal. The boys are ribbing him about that in the dressing room.
"But he's a hard-working boy who is desperate to do well and that's important. He's someone who used to get up and work at 7.30am as a roofer so it's good to have someone like that in the squad - a squad which rolls their sleeves up and wins you football games."
Coventry were the better side in the first half but could have been behind in the 10th minute when Marcel Seip's header rebounded off the post.
Minutes later Plymouth were the side thankful of the woodwork when a deflected header from a Danny Fox corner hit the upright.
The best chance of the half was a 30-yard drive from Fox in the 32nd minute, which forced a good save from Romain Larrieu.
Both sides were struggling to carve out opportunities before and after half time and after 20 minutes of second half inactivity Coventry manager Chris Coleman decided to introduce Guillaume Beuzelin and Freddy Eastwood, while Sturrock brought on Noone and Steve MacLean.
Eastwood nearly played a part in breaking the deadlock minutes later after laying the ball off for Simpson to feed Clinton Morrison but his shot from eight yards was too high - a miss which was to prove costly.
"Our attitude was better this week and if we'd taken that chance, we probably would have gone on to win the game," said Coleman.
"I was pleased with our tempo early on in the game and I knew Plymouth would come here, get men behind the ball and look to hit us on the counter. My only criticism was our lack of imagination.
"If we'd have come in and got a 0-0 draw, you might say that is something we can build on. But the only way we are going to build up our confidence is by winning games."