Northampton are on a dismal run, with the 50-21 defeat to Harlequins on Saturday their seventh Premiership defeat in a row, and Hartley has taken the brunt of the criticism.
However, Jones says Hartley will not let his problems at club level affect his role as England captain as they prepare for the forthcoming Six Nations campaign.
"He loves the club, he had a great relationship with Jim Mallinder and now Jim's been sacked, it's a difficult time. Their form's not great and he carries a lot of weight," Jones said.
"But he's got a clear role with England and that's to be captain and to be the leader. He understands that. His value to us is as captain and he'll be a fine captain for us.
"Is Joe Root the root of England's cricket problem? No, he's not. Certainly captaincy is an issue and I'm sure he can improve his captaincy, but you can't just look at one thing and say 'this is the issue'."