Left-back Jacobson, promoted to stand-in skipper for the last two games with regular captain Matt Richards left on the bench, struck from 20 yards in the 49th minute to sink one of his former clubs.
Turner said: "The ball usually finishes out of the ground when Joe takes a free-kick. I was just moaning he's only taking one stride where I thought he needed a little bit longer run up but it was a good strike in the end.
"I think he's risen to his role as captain. I think he's put in two tremendous performances as well as the goal and that might have just given him that little bit of responsibility by skippering the team."
Turner was pleased with the display of his side, once again packed with young players to provide energy, as they climbed above Oldham in the lower reaches of the League One table.
"We had a very good second half and should have added to the total," he added. "We should have been out of sight before there was any anxiety late on in the game. We showed a lot of energy for this stage of the season, a lot of brightness in our play in the second half.
"Oldham came here and worked very hard and we had to match that but in the end we played some good stuff, some real pacy football and I was pleased with the manner we performed."
Oldham manager Lee Johnson, tasting defeat for the third time in nine games since taking over at Boundary Park, admitted his team's performance disappointed him.
"We've had some proper home truths in the dressing room which is good because we'll now see who can react to that and who can't," said Johnson.
"If you want to win a league or compete to win a league you have to show in every game more than we showed here. I was actually sitting there and all it did was confirm things that I already knew."
- Sports & Recreation