The 29-year-old Saracens winger was omitted from the 32-man England squad that will tour Australia next month.
Ashton helped his club win the European Champions Cup and reach the Premiership final, but Jones feels Harlequins' Marland Yarde is a "better fit".
"There are parts of Ashton's game we're not happy with," he told BBC 5 live.
"We've spoken to him about that and if he can fix that then he can get in the squad."
When asked whether Ashton, who has won 39 England caps, needs to improve defensively, Jones said their conversations were "private".
Ashton missed this year's Six Nations campaign after being given a 10-week ban for making contact with the eyes of Ulster's Luke Marshall during a European Champions Cup game.
He has scored 10 tries since his return, but the England boss suggested 24-year old Yarde, who crossed seven times this season, could have matched that feat given the opportunity.
"Marland's got a good, strong all-round game, great coachability. I think his best rugby is ahead of him," added the Australian.
"Ashton's done very well to score a lot of tries in a very strong team. You've always got to look at it in the context of what side they're playing for and the opportunities they have.
"He has done some good work. It's all relative to the strength of the team you're playing in and there are other areas of the game apart from scoring tries."
New Zealand-born centre Ben Te'o, who will join Worcester from Leinster before the England party leaves for Australia, is one of four uncapped players named in the squad.
The 29-year-old switched codes in 2014, having represented Samoa in the 2008 Rugby League World Cup and won a National Rugby League title with South Sydney Rabbitohs.
Jones, who said Manu Tuilagi is expected to undergo scans on a hamstring injury on Monday, is pleased to have Te'o as an option.
"Ben's a very talented player," said the 56-year-old. "He can play through the line, he's had a great season for Leinster. He's a big guy and he hits hard.
"Since I've taken the English job and known he wanted to play for England and qualifies for England, I've watched him carefully.
"I've kept in contact with him and he presents a great option for us at 12."
Props Ellis Genge, of Bristol, and Harlequins' Kyle Sinckler have been included in Jones' squad, along with Northampton back row Teimana Harrison.
Jones says both of the uncapped props have a "competitive edge".
He added: "Both aren't ready to scrummage at Test level but both have got potential, so we need to bring them through.
"Genge is a boy that's not afraid of anything and that's what we need to beat Australia. He's aggressive and he can run with the ball and he's got that bit of an edge about him."
The former Australia and Japan head coach continued: "Harrison has been absolutely outstanding for the Saints.
"The robustness of his play, his physicality and his ball carries, his low tackling and his coachability make him a great player to add to the squad.
"He's got a hard back row to break in to. Robbo [Chris Robshaw], James Haskell and Billy [Vunipola] obviously did well during the Six Nations and there's no reason they can't continue to play well."
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Chris Ashton needs to "fix" parts of his game before he can expect to be selected for England again, says head coach Eddie Jones.