The Nerazzurri are chasing a 14th final appearance, and a possible eighth title, but two-time winners Bologna are in ominous form in Serie A and full of confidence.
Stramaccioni is suitably wary of a side that ousted cup holders Napoli from the last 16 before trouncing Chievo 4-0 on Saturday night.
He told inter.it: "I believe Inter will approach the Coppa Italia the respect it deserves. For us it is as important as the league and the Europa League and we want to go as far as possible.
"We know all too well that we are meeting an in-form side but most of all that this is just one game. We have already seen Napoli bear the brunt of what Bologna can do - they are a tricky opponent.
"It will be a match that needs intense concentration and we will battle right to the end."
Rossoblu boss Stefano Pioli is eager to seize the opportunity to move one step closer to a first final appearance since 1974.
"I want everyone to perform well," he told bolognafc.it. "We have prepared well and are ready for Inter, who have great players and a great coach.
"I want my players to remember how they felt before, during and after Saturday's match.
"But the quarter-final is a separate game and we have to approach it in the best way possible."
The winner of Tuesday night's game will book a two-legged semi-final against either Fiorentina or Roma, with the Giallorossi left angered over a late switch of venues.
Lazio's progression to the last four at the expense of Catania meant Roma could not use the Stadio Olimpico for Wednesday's game, as was originally scheduled, and the capital club lost the subsequent appeal against the decision.
Roma have suffered back-to-back defeats in the league and chief executive Claudio Fenucci wants the players to provide some cheer at the Stadio Artemio Franchi.
He said: "We have players with potential at Roma. The rejuvenation process takes time but we are convinced that we are on the right track."
Rome are as highly decorated as Juventus in this competition, having won the Coccarda nine times, slightly edging the Bianconeri on final appearances by contesting the cup on 16 occasions to Juve's 14.
Fiorentina, meanwhile, are aiming to reach the May showpiece for the first time since 2001, when La Viola managed to defeat Parma 2-1 over two legs.
Vincenzo Montella's men have also lost two games on the spin, most recently going down 3-1 at Udinese, but the Fiorentina boss remained philosophical afterwards.
"I am still optimistic," he told La Repubblica. "I don't think we can lose yet another game playing as well as did here and last Sunday."