The Nerazzurri sit 10 points behind city neighbours AC Milan, who currently hold third spot, having lost their two Serie A matches either side of the international break.
Losses to Bologna and Juventus sandwiched a 4-1 victory over Tottenham in the Europa League but Inter still exited the tournament on away goals.
A win on Wednesday night would see them leapfrog Lazio into a qualification spot for that competition again but Stramaccioni is still aiming for a place in Europe's elite club contest.
He told www.inter.it following Saturday's 2-1 loss to Juventus: "Is it beyond us now? Of course it's not.
"We played an open game today. We're playing better, we have a match in Genoa now and we have to win it."
That sentiment was echoed by veteran midfielder Javier Zanetti, who added: "We need to find the strength to do as best as possible in the remaining games, find the strength to put in a good performance in Genoa like we did today against a top team like Juventus.
"Third place? We still have a few six-pointers to play and a game in hand.
"Let's see what happens between now and the end of the season."
A win for the Genoa outfit would see them jump into the top half of the Serie A table and effectively end any worries of relegation.
The match was due to be played on March 17 but was postponed after heavy snow and rainfall was forecast.