Totti has opined that Roma do not have the quality of players Mourinho requires to make the capital club great again.
Roma are currently seventh on the Serie A standings, having lost four of their last six games in the top flight.
After the Giallorossi lost 3-0 to champions Inter Milan over the weekend, Mourinho took his frustrations out on a journalist and cancelled his post-match press conference.
Totti wants the club to back Mourinho in the transfer market and give him time to build a competitive side.
"To win you need the [right] players," said Totti, who is Roma's all-time leading appearance maker and scorer.
"To win it takes an important manager. It takes a club that makes you feel at home at every level of your employment here.
"They have to be always available for everyone here but the most important thing, as we all know, if you want to win you need the players. It is a necessity, the foundation [of victory].
"I don't want to disrespect our current squad now, because it is an important squad with important players. But there are no 'champions' [world class players], and this is plain to see. Only good players who can do well in a certain context."
Totti added: "When we talk about Roma, I feel huge emotions.
"As a fan, I can say we are not in a great period but 'if you are not Roma, you don't suffer', this is our motto as we say and I guess we are used to it, to these topsy-turvy seasons.
"But I am sure the board and the gaffer [Mourinho] want to put back a smile on us fans' faces. A city like Rome deserves respect and most luminous stages than what we are watching now.
"Give them time... but not too long and hope we can see Roma back to shine at international level."
