Speaking to Mundo Deportivo, the Spain forward acknowledged the blow provoked by the 41-year-old's decision to vacate his post after seeing the Catalans' relinquish their Liga and Champions League titles.
However, he shared his optimism at Vilanova's appointment, saying the former assistant has all the attributes required to make the step-up and deal with the pressure that awaits him in his new role.
"Tito [Vilanova] will be a good coach," Pedro told the publication.
"He has a playing philosophy that is attack-minded, he wants our football to be pleasurable to play and watch. On top of that he is a great person.
"It is true he will have to evolve insofar as he used to organise the training sessions while withdrawing a little in the locker-room, and he is now expected to fill Pep [Guardiola]'s boots and talk to us before and during every game.
"But in my opinion he is perfectly capable of taking hold of the squad. He has a strong character and he has the quality to get us back to the top."
Vilanova will officially become Barcelona's new head coach on July 1, when Guardiola's contract expires.