Keita Balde gave Lazio the lead just 12 minutes in before a Daniele De Rossi equalised from the penalty spot. But Simone Inzaghi's side went back in front through Dusan Basta before Keita added another to get the better of their city rivals.
And Spalletti feels the opening goal was the key moment, leading to further issues for his side.
“Ugly incidents led to an ugly Roma," Spalletti told reporters afterwards. "We started off playing the way we thought that we had to play and created chances, but Lazio scored with their first attempt.
“Of course it was a psychological blow, you make mistakes and it becomes a wide open game. We were no longer the team we know that we are.
“I opted to go with three at the back after a while, as Lazio were dangerous on the counter and lacked sharpness. Then Lazio scored again with a deflection, so we were unlucky.
“If you look at the game today, we were weaker in defence. After a result like this, you have to accept all the criticism. We lost sharpness, made bad decisions, were unlucky on the incidents, as both the first and second goal were deflected shots from the edge of the box.
“We created six or seven chances that we failed to convert. We should’ve kept more possession, as we did in the opening 10 minutes, and that would’ve worn Lazio down, making it easier for us to break them down. Instead, by taking the lead, Lazio could simply counter.”