Team GB finished the four-man event in fourth place, finishing 0.11 seconds off the United States in third.
"Overall it has been a great race and to only finish 0.11 seconds off the medals is amazing," Jackson told BBC Sport following the fourth and final run.
"Just being involved in such a great race makes it enjoyable. I would like to stay on for another year depending on what the Royal Navy and Royal Marines say.
"I'm happy to keep working with this boys - the future is bright."
THe Russian Federation, led by pilot Alexander Zubkov, won the gold medal with a combined time of 3:40.60.