Buffon was livid with the decision and protested extensively, which resulted in him being sent off by Oliver before Cristiano Ronaldo dispatched the spot-kick past Wojciech Szczesny to send Real through.
We will still need to meet some objectives.
Former Juve captain Del Piero has since been criticised by fans of the Serie A champions and the 43-year-old used Twitter to hit back.
Gianluigi Buffon argues with referee Michael Oliver.
"If we don't win the Scudetto and Coppa Italia they might not still want me".
"I'm sure Oliver will have a great career in future, but he's too young to officiate a match like that".
Napoli beat Milan earlier this season before Gennaro Gattuso took over from Vincenzo Montella, with the club now sixth, eight points off their Champions League ambitions with just seven games to play.
It also finished goalless in the Rome derby as Lazio and Roma remained third and fourth in the table respectively.
Lazio crashed out of the Europa League after losing 4-1 to salzburg in Austria on Thursday night despite winning 4-2 in Rome last week.
There was nothing to separate them in a tense derby, however - despite a late red card for Lazio's Stefan Radu - at the Stadio Olimpico as both teams moved to 61 points with Lazio ahead of their neighbours in the standings on goal difference.
Roma are riding high after a insane night at the Stadio Olimpico saw them beat Barcelona 3-0 to reach the Champions League semi-finals, thanks to Edin Dzeko's away goal.
At the time, he said: "Certainly I will go overseas".
- SANA: Syrian air defenses repel strike on Shayrat air base in Homs
- Today's Brokerage Rating: Marvell Technology Group Ltd. (NASDAQ: MRVL)
- Anheuser-Busch InBev SA/NV (BUD) has analyst mean rating score of 2.00
- Trump Set to Nominate Richard Clarida, Michelle Bowman to Fed Board
- Zayo Group Holdings, Inc. (NYSE:ZAYO): Quant & ROIC in Focus
- Karl Lagerfeld Slams Models Who Complain About Groping in Controversial New Interview
- Cisco Systems, Inc. (CSCO) - Stock under Review
- Man City win Premier League title
- Twitter reacts to Bryce Harper's broken bat home run
- Trump's personal lawyer due in NY court