Inter needed to better Tottenham's result against Barcelona to progress to the last 16, however, Spalletti's men slipped into the Europe League following Spurs' late point at Camp Nou.
Head coach Spalletti bemoaned what transpired at San Siro, telling Sky Sport Italia: "We were unable to keep our calm, despite the fact everything was still possible. We gave the ball away, were tactically not organised and PSV were allowed some dangerous counter-attacks.
"As the anxiety grows, you lose sight of how to control the game and it became end to end. We had our chances to score, but it wasn't the right attitude we needed in that moment.
"Not every team can beat anyone. This does weigh on our psychology and we had to keep the game in the balance, but we became too frenetic after going a goal behind.
"Naturally, the crowd cheers and the players look around to see what happened. UEFA asked if I wanted to have the results from elsewhere pop up on the screen and I said yes. A team like Inter needs the mental strength to handle that situation.
"It's not one player who can change the overall attitude of a team, it's a much bigger picture. We must do everything together, as it's the only play to play like a unit.
"It's easy to look back and say there are moments when we could've done better, but once again we let the tension get to us and didn't handle the situation well.
"There is disappointment, the same as any other club that goes out of the Champions League."
PSV finished bottom of the group with two points but boss Mark van Bommel said: "I think we played very well in these last six matches in the Champions League.
"We've grown as a team. A couple have players now play in the national team. That's the biggest benefit of this season: the progression we make. We rewarded ourselves a little bit with this draw. These signals are good for our internationals."