Tavecchio, 71, was announced as the new president on Monday after collecting 63 per cent of the final-round votes.
He drew heavy criticism last month for reportedly referring to African players as 'banana eaters'.
Tavecchio said he had learned his lessons before adding he would make the most of "an era where words and appearance are more important than thoughts and essence".
"I'd like to thank those who have bestowed their faith in me and who have granted me their continuous support and contribution even in difficult times," he said.
"But I would also like to thank those who had legitimately carried out different evaluations. I want to be, and I am sure I will be, everyone's president, especially of those who had expressed dissent towards my candidacy.
"I can fairly state that I will draw many teachings from what has happened in the last few weeks.
"And I am sure that I will take advantage of that in an era where words and appearance are more important than thoughts and essence.
"Also, I will try to combine better my way of being, a bit rough and with no glamour, as somebody has fairly defined it."
Tavecchio called for togetherness at the federation, saying that was the only way they would achieve their goals.
"The reforms to our system can only be accomplished together," he said.
"As I have stated in my programme, there are no 'providence men' here and nobody has a magical recipe."
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