The Blades' arch-rivals Sheffield Wednesday became the first side in 95 years to secure a Sheffield derby double with a 2-1 win at Bramall Lane in February following a 1-0 success for the Owls at Hillsborough in October.
Blackwell's season then ended in ultimate heartbreak after his side was denied a return to the Premier League after being edged out by Burnley at Wembley.
Blackwell said: "Obviously this season has had two massive low points, losing twice to Wednesday was one and the other one was the final.
"To lose to your rivals and see a record of 90-plus years go too was a massive downer.
"You don't like losing to your enemy and there isn't a bigger one than Wednesday for us."