The Dons will finish the Clydesdale Bank Premier League campaign in the bottom half of the table after failing to make the top six before the split.
"The season has not really gone to plan. We did not get in the top six again," Considine told RedTV. "We knew after the quarter-final that the bottom six would be where we would end up so everyone has been looking forward to Saturday's game since then."
Victory at Hampden would allow them to take a major step towards claiming silverware, as well as securing a Europa League berth next term if champions Celtic win their own semi-final on Sunday.
"It is the last chance saloon to get into Europe, which would be great," Considine added. "It is a couple of years since we have played in Europe. That is really where we feel we should be."
Aberdeen's recent record at the national stadium may be less than impressive - they lost 4-0 to Celtic in last year's semi-final - but Considine knows the expectations of those who make the long trip from the Granite City will be high.
He said: "The expectation is there because Aberdeen is a massive club and people expect us to be winning cups."
Hibs have also endured a tough season and are still battling to secure their SPL survival, but Considine insists league form will have no bearing on the cup tie.
He said: "They have players who can produce a bit of magic to win you a game, but so do we."