The British crew finished fifth in the four-man event, 0.11 seconds off third place.
The 36-year-old told BBC Sport: "It's hard to think we've come so close to a medal. Hopefully this will be enough to secure backing [from UK Sport] so we can continue to progress.
"For a split second I thought potentially I may not be here [after suffering a ruptured Achilles last summer] but the support I've had from my teammates since day one has been amazing."
Jackson has said that he intends to continue competing for the next couple of seasons, but does not expect to compete in Pyeongchang in 2018.