The Blucerchiati had never before lost at home 3-0 to their local rivals.
"If we take the right lessons from this, then it can be a good defeat for us. We were too bad to be true tonight," Rossi told Sky Sport Italia.
"We've got to work harder and better, because this is not good enough. I hope it was a one-off that we got wrong and I apologise to all the fans. I take responsibility as the Coach of this squad.
"We knew Genoa would play this way, but they did well to make the most of their opportunities and deserved the victory.
"We did badly in terms of technique. It's true this isn't the most scintillating side, but it is certainly better than this."
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