"I set no limits, it all depends on how much we can improve. First of all, inside ourselves," he told Italian newspaper Corriere della Sera on Tuesday.
"We knew there was a chance to find a group with strong teams; unfortunately, this happened.
"The only way to go through is to play high-level games. Spain, Albania and Croatia will not be happy anyway as they got Italy from pot four.
"It only depends on us, we are Italy."
Spalletti's side will start their campaign in Dortmund against Albania on June 15th before facing Spain five days later and Croatia on June 24th.
"With this environment... and the passion of players in whom I believe, we should not see any wall as insurmountable," he said.
"I'll repeat what I told my Azzurri before a difficult game: There are many things that used to scare me from the outside, but after facing them, they excite me."
Spalletti was keeping his cards close to his chest about his squad selection, but said he would look for certain characteristics in his players.
"I want guys who believe in it, who feel the responsibility as I do, proving that they want to make history," he said.
"We must give back to Italy the love they feel, make the whole country celebrate and unite people.
"The Azzurri shirt must be desired and honoured like a sacred object."