The Stadio Franchi crowd chanted and jeered at the final whistle in the 2-2 draw with Catania, which extended their winless run to four games.
"I am sorry for the fans, who really don't deserve these results, and I understand their disappointment," Della Valle told Radio Blu.
"However, Mihajlovic's job is not up for debate. Sinisa has no blame for what happened this evening.
"The table remains very tight, so we're right up there near to the top. Of course everyone wants to win and we are slowly studying a way to make it more entertaining for our fans, but we have the right ingredients to have a great season."