His comments came after being held to a goalless draw by Turkey in a warm-up friendly in Bologna on Tuesday.
The Azzurri were poor in the first half but showed more spark after the break.
“I expected us to struggle a bit, given the fitness work we’ve done,” said Spalletti, who must trim his squad down from 30 to 26 players by Monday.
“But I thought and hoped we would put more quality into managing the ball, both in the opponent’s half and in our own.
“Too much possession was given away, we were too far apart and so our less-than optimal condition of fitness was more noticeable.
“We need to do better, but I know this group in depth and we will go to work in depth, because we need to grow [and] improve the quality [of our play] in order to also improve the intensity.”
Italy start their Euro 2024 campaign against Group B rivals Albania on June 15.
They take on Bosnia and Herzegovina in another friendly in Empoli on Sunday.
ANSA