Lazio, who took the lead through Ciro Immobile's first-half penalty before conceding twice in the second half, are 10th in the table on 17 points, their worst start to a Serie A season since 2013/14.
Sarri pinned the blame on the players' attitude and mentality and said that if he felt his management of the team was part of the problem then he was willing to step down.
"Something has to be done to break this inertia,” Sarri told reporters after the game.
"The squad has lost character and initiative. After scoring a goal in the first half, we came back out hoping to control it for 50 minutes. That is not what our characteristics are as a team.
"If over the next few days I evaluate and find that it is my fault, I will be the first to take the decision to walk away by speaking to the President."
Despite their poor start in Serie A, Lazio are second in their Champions League group with seven points, one behind Atletico Madrid and one clear of third-placed Feyenoord.
They host bottom-placed Celtic on Tuesday.
"I am worried by the mentality of a team that struggles to find itself again," Sarri added.
"Sometimes the Champions League can perform miracles and hopefully provide a different mentality."
