The Shakers eventually succumbed 3-2 on spot-kicks in their second-round replay after finishing 1-1 at the end of normal time on Tuesday night.
Being held up in traffic following an accident did not help their preparation for the tie, and Bury were then thwarted on the field by Shrimpers' stand-in goalkeeper Daniel Bentley, who produced a matchwinning performance with a string of top drawer saves in normal time and also two penalty stops from David Worrall and Mark Hughes in the subsequent shoot-out.
Blackwell said: "It was a long way to come down and to lose on penalties is very disappointing.
"It is a bit of a lottery when it goes down to that but Daniel Bentley made some terrific saves in the match and won it for Southend with two saves from the spot.
"It took us 10 hours to arrive as we were stuck in an accident and it just sums up the game and our luck."
Bury took the lead in the 59th minute, following a rare mistake from Ryan Cresswell. The towering Southend centre-back gave the ball away in his own penalty area and that enabled Andy Bishop to tee up Zac Thompson and he made no mistake.
But Bury were in front for just four minutes as Gavin Tomlin headed the home side back level.
The in-form forward was picked out by an excellent right-wing cross from Sean Clohessy at the near post and nodded the ball into the left-hand corner.