Liverpool got the better of the Premier League champions in the International Champions Cup, winning 3-1 on penalties, with the England international netting in normal time.
It was a rare goal for Henderson, who had only managed a total of five in all competitions last season but Rodgers has challenged the 24-year-old to hit double figures in the new season.
"That's the objective for Jordan [to get more goals]," Rodgers told reporters after the game. "The finish he produced to get the equaliser, he does that day in, day out in training.
"He's a player that is so fit and strong, and he's such a team player - he does a lot of unselfish work. This year we're asking him to get more into the box.
"I thought he had more opportunities when he played just around the corner [of the striker] in the last 20 minutes of the game - he was able to time his runs better going forward and he got in a few times.
"That's his strength - he can really penetrate the defensive line. I would expect him to be getting up to 10 goals this season because he has the quality and tactical awareness to arrive into the area to do that."