The Roma midfielder scored in victory over Armenia last week.
Totti said, “I am not surprised by Pellegrini's improvement, as I've always known Lorenzo was phenomenal. Now it's up to him to keep going at this level.
“Along with having been a fantastic player, Roberto Mancini is also proving himself to be a great Coach with different capabilities to many others. He has a good group to choose from, with many talented young prospects. I think Italy can have their say at Euro 2020."