Jones has netted just twice in 107 appearances for Blackburn, United and England and, despite spending much of his time in defence, is eager to improve his record.
He had two headed opportunities in the 1-1 draw with Arsenal at the weekend and was particularly disappointed not to convert the first, a cross from Robin van Persie.
"The first one was easier, I think I should have put that one away," said the 21-year-old.
"The second chance was a bit more difficult. If it had been in the air for a couple more seconds, I might have got on the end of it with a cleaner connection.
"Scoring is probably something I need to work on. Hopefully I'll get one before the end of the season."
Jones had mixed feelings about the point gained from the Emirates Stadium clash, after Arsenal had the better of the first half before United came back strongly.
"In the first half, I would have said a point was a good result," added Jones.
"But having seen what we put on in the second half, we are disappointed not to have come away with all three points.
"Full credit to Arsenal, they took us by surprise and came at us all guns blazing in the first 15 to 20 minutes. We couldn't really get a grip on the game .
"But once we got on the ball with Michael Carrick, Wazza (Wayne Rooney) got in the pockets and we got the ball wide to Nani and Antonio Valencia.
"The manager said at half-time that if we created more chances, we'd win the game. We created three or four and perhaps could have stuck one or two more in."