The Giallorossi opened their league campaign with a thrilling 3-3 draw at home to Genoa after surrendering the lead on three occasions in the Italian capital last week.
It was a busy off-season for Roma, who hired head coach Paulo Fonseca and signed Leonardo Spinazzola, Amadou Diawara, Pau Lopez, Jordan Veretout and Gianluca Mancini following last season's sixth-place finish.
Roma, meanwhile, lost star defender Kostas Manolas, Luca Pellegrini, Daniele De Rossi, Stephan El Shaarawy and Steven Nzonzi.
Club great Totti - who left his role as Roma director in June after a 30-year association with the organisation - said Fonseca's side have a battle on their hands to qualify for the Champions League ahead of the Derby della Capitale against Lazio.
"Simone Inzaghi has put together an excellent Lazio, even if Roma are stronger on paper. They are to be feared," Totti told Radio Radio ahead of Sunday's match.
"This is certainly a different type of season for me, as watching Roma play on television on Sunday made me think. It's my decision and I continue to stand by it, but as a fan I hope the club can do something more in the final few days of the transfer window to ensure Roma can at least compete for a place in the Champions League.
"I hope that I'm wrong, but when you've been in football for 30 years, you have a good eye. I think many fans like me hope to see a great Roma that can get back into the Champions League and hope the club is working in that direction.
"I think the top three are already decided, then anything can happen after that. Unfortunately, Roma can only hope to fight for fourth place. That is the reality of the situation, seeing what happened in pre-season.
"Napoli and Inter can trouble Juve to the end, but we all know that when they need to step on the gas, Juve do it all the way."