The Spaniard, who left Liverpool by mutual consent after six years in charge, has the unenviable task of trying to match Mourinho's stunning success in winning an unprecedented Italian treble last season before quitting to join Real Madrid.
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"Mourinho has done a great job here, but I'm different. I like to win, to play well if it's possible," Benitez told a packed news conference at his unveiling on Tuesday.
"My objective is to keep a winning mentality and play good soccer."
Mourinho, whose style of play was sometimes defensive, upset Inter fans by jumping ship in their finest hour and taking some of the gloss of their Champions League final win over Bayern Munich by announcing his departure almost straight away.
Benitez, who speaks decent Italian, has only signed a two-year deal at Inter but he played down speculation he would definitely not stay beyond 2012.
"I'm sure I will stay longer, if I do well," he said.
His first objective will be to cling on to his top players with right back Maicon indicating he would like to join Mourinho at Real.
Portuguese winger Ricardo Quaresma, who endured a tough two seasons at Inter, has moved to Turkey's Besiktas.
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