Flight Instructor reported the student lost control of the aircraft during landing resulting in a runway excursion.

Narrative

While practicing landings with my student at ZZZ on RWY XX we ran into the grass. Upon landing we landed left of centerline with a little too much airspeed and began aggressively rollings/drifting to the left of the runway directly into the grass. As I took flight controls we were partially in the grass and I put in right rudder to try to correct to get back on the runway; however I did not remember to reach for the hand brake located in the left seat as I do not have toe brakes in the right seat and the plane did not slow down to come to a complete stop. It continued to then roll into the grass on the right side of the runway.I believe that I should have called a go-around when it looked like we were landing too far from center line. I also believe that my initial instincts (from about 416 hours worth of training in an aircraft with dual toe brakes) thinking that I was pressing on the rudder & brakes simultaneously would allow the plane to slow down; come to a complete stop and get re-centered was the cause of why we ran off to the right into the grass. Because while I was thinking I was pressing both the rudders and the brakes I actually was not. In the moment I did not recognize/remember that I did not have toe brakes on my side to slow the plane down; only a hand brake. If I would have used the hand brake the plane would have slowed down and came to a complete stop before running off the runway.While flight training can take place in any airworthy aircraft I think it would be a safer environment if that specific training aircraft had dual toe brakes (brakes on both left and right side)- in case of critical situations the CFI can easily have full access to all controls including toe brakes.