The Aquile were 4-1 up at one stage, before Benevento's fight back.
“We did really well in the first half, but we could have killed off the game earlier," Immobile told Sky Italia.
“We lowered our guard in the second half and this is the result, we must learn from our mistakes, that's how we can improve.
“I am satisfied with the goals and the victory. Our target is there," the Italy striker added.
Immobile broke a two month scoring duck on the day.
“The team needs my goals, and I live for goals too, but I am not obsessed. I scored thanks to the help from my teammates. We are not going to give up. We must be ready for anything to qualify for the Champions League."