The two Milan clubs share the San Siro field and Milan played "at home" on Friday in front of a huge partisan crowd.
"The fans' behavior was unfair to [Inter president] Massimo Moratti ... Milan was not as sparkling as usual because the team probably was already thinking of Barcelona," Italian premier and AC Milan owner Silvio Berlusconi said.
The match was moved to Good Friday, amid protests by Vatican officials, to give AC Milan an extra day to prepare for Tuesday's Champions League first-leg semifinal against FC Barcelona.
Coach Carlo Ancelotti had originally planned to rest Shevchenko and Kaladze. He changed his mind hours before kickoff, saying his players had time to recover by Tuesday and that second place was going to secure the club more money and automatic qualification for the next Champions League.
Mancini's plans were somewhat upset when he was forced to replace injured Sinisa Mihajlovic with Marco Materazzi early in the first half.
Striker Samuel Eto'o scored the only goal to help league leader FC Barcelona beat Villarreal 1-0.
The match could have presaged next month's Champions League final, but both teams had key absentees.
Barcelona was without star midfielder Ronaldinho, who also missed last weekend's draw against Santander with a right thigh injury.
Captain Carles Puyol was able to play, following Barcelona's successful appeal against his suspension on Thursday. Barcelona is set to meet AC Milan on Tuesday in a Champions League first-leg semifinal.
Villarreal, enjoying a sparkling Champions League debut season, plays Arsenal in London next Wednesday, and coach Manuel Pellegrini chose to rest Argentine midfielder Juan Roman Riquelme, who spent the 2002-2003 season at Barcelona, striker Diego Forlan, and goalkeeper Sebastian Viera.
Not as successful in La Liga, Villarreal still hopes to rise from eighth place into the top six to secure at least a UEFA Cup berth in case it misses out on Champions League glory.
Barcelona's win increased its lead in the standings to 73 points, ahead of Valencia and Real Madrid with 59, and Osasuna on 58.
Eto'o controlled the ball with a delicate first touch just outside the penalty area, advanced three paces and struck a right-footed shot just inside the left goal post in the 11th minute in typical, predatory style.
RSS