Many Blues fans were vocal in their opposition to the interim appointment of the Spaniard because of a long-standing antipathy dating back to his time as manager of Liverpool.
Benitez, appointed after the dismissal of Roberto di Matteo in November, helped Chelsea to a trophy in the Europa League and guided them to third place in the Barclays Premier League.
And he told the Sun: "A lot of fans supported me in the end. Maybe some of them couldn't change their minds. You can only win trophies at the end of the season. You cannot win them in the first month with a new team.
"You have to be patient but in football that's more difficult. But we did our job and I hope everyone could enjoy it. We did what we had to do - that's the main thing."
Benitez has been widely tipped to take over at Napoli, whose coach Walter Mazzarri left at the end of the season to join Inter Milan.
He said: "I want to be back in work quickly, yes. But I will go back to London and be with my family for a while."
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