Gasperini was left angry and disappointed with his side's 4-3 defeat at Palermo in Sunday's Serie A opener.
"It's obvious that after our performance at Palermo, we need to correct certain things," Gasperini said. "We lacked balance and we made huge mistakes against them.
"We will try to make sure we don't repeat those mistakes tomorrow [Wednesday]."
Inter have won just one of their last five opening games in the Champions League and Gasperini hopes to change that trend.
"There's only one acceptable result for us tomorrow [Wednesday] against Trabzonspor," Gasperini said.
"We will try to get a win while also producing a good performance in front of our home fans."
Gasperini has warned his players not to underestimate tournament debutants Trabzonspor who finished runners-up in last season's Turkish league.
"Trabzonspor are a good team," he said. "We have watched their recent games.
"In the Champions League every game is difficult.
"We cannot take this game lightly and think it will be easy to beat them.
"Trabzonspor have quality and speed.
"Despite their absences, they are a tough team to beat."
Trabzonspor travel to Milan on the back of a 1-1 draw to Mansaspor in their Super Lig opener.
The visitors are without attacking pair Burak Yilmaz and Adrian Mierzejewski, both suspended.
To complicate matters for the Turks, coach Senol Gunes will serve his first of a two-match touchline ban on Wednesday.
Gasperini is set to hand Dutch winger Wesley Sneijder a place in the starting XI, with new summer signing Diego Forlan ineligible to play in the group stages of the competition.
Sneijder, who came off the bench in the loss to Palermo, is set to play in support of Argentinian forward Diego Milito.
The hosts will be without Cristian Chivu, Ivan Cordoba, Maicon, Thiago Motta and Emiliano Viviano, all sidelined through injury.