Inter succumbed to a Patrick Cutrone strike in the 105th minute as Milan triumphed after extra time at San Siro on Wednesday.
After an unbeaten start to the season, Inter have gone off the boil with just one win in five matches in all competitions amid three consecutive defeats.
"We've lost a bit of confidence, we do things with less conviction in our quality," Spalletti told Rai Sport.
"When chances come along and you don't take them, that's just a fact. We must give the right importance that they deserve. Then when you concede something, you let in a goal.
"On a psychological level, we must turn a corner, realise that we ought to do more. The players are involved, then when you can't even convince them using facts that the situation is like this, you must find a way to make them understand.
"In physical terms, they are fine, the quality is there, but if you expect someone to resolve your problems, then it all becomes difficult. We must resolve things ourselves, as if you wait for someone to do it for you, then you're in trouble.
"I think this side has the potential to beat any opponent, but must realise its capabilities and use them every time. In some moments we are not complete and don't give the best individual performances, so if a few of those are lacking, it becomes difficult for the whole team."
Out of the Coppa Italia and third in Serie A — five points adrift of leaders Napoli — Antonio Candreva said: "We are missing a bit of good luck. The last two defeats were painful, as we got the second half wrong against Udinese [3-1] and didn't make the most of our chances at Sassuolo [1-0].
"We must focus on Lazio now, as that is a fundamental game for our season.
"Morale is low at the moment, as we wanted to go all the way in the Coppa. From tomorrow, we must get back on track and unite as a group."