The Buddies claim that the decision over the extra seats in Hampden Park's West Stand was made without their knowledge.
A club statement read: "We are bitterly disappointed that this decision has been made when there were still nine days to go to the final and also while Hearts do not appear to have sold their full allocation.
"We feel strongly that any decision on these tickets should have been delayed until closer to the final.
"We were advised earlier this week that the SFL were considering an option to split the remaining 3,500 West Stand tickets between the two clubs and also allocating more South Stand tickets to ourselves to make up some of the shortfall."
The two sides are separated by just a point in the SPL and St Mirren came out on top 2-0 when they last met on February 27.