Milan have won just two of their past 10 matches in all competitions, leaving them battling in 10th spot in the league.
Inzaghi is under increasing pressure at the helm, with his team now 10 points off qualifying for the UEFA Europa League.
"We're a team right until the end. The coach isn't the only one responsible for the situation, but us players too," he told reporters.
"As I've said before, we have to improve to come out of this situation together.
"My future? I'm currently a Milan player. We shall see for next year.
"I haven't seen many of Cagliari's matches. Every match is hard for us at the moment."
But they conceded twice in seven minutes late on against Vincenzo Montella's side.
The situation for Zdenek Zeman's side is becoming increasingly desperate, sitting four points behind Atalanta and eight adrift of 16th-placed Chievo.
Of the 33 matches played between the two clubs, Cagliari have won just two – losing 21 and drawing 10.
Cagliari's last win over Milan came in 1998.
Zeman's men need a win in their relegation fight, while Inzaghi must lead his side to victory to ease the pressure on his job - for the time being at least.
