The experienced midfielder helped Roma to a 2-0 win over Fiorentina on Saturday as Rudi Garcia's side got their campaign off to a winning start.
Goals from Radja Nainggolan and Gervinho ensured maximum points for last season's runners-up.
De Rossi feels his team-mates have the capability to prove a thorn in the side of Massimiliano Allegri and co - as Juve eye a fourth consecutive Scudetto.
"We intend to annoy Juventus, even though we know this is just the beginning," he told Sky Sport Italia.
"Watch out also for Milan, Napoli, Inter, Lazio and Fiorentina as they'll fight to the end too."
Roma were made to work hard by former player Vincenzo Montella and his Fiorentina side - with Gervinho's late goal settling any nerves at the Stadio Olimpico.
However, De Rossi was not concerned by their second-half lull, insisting Roma will improve.
"I think our drop in intensity towards the end was normal, considering it was the first official game of the season," he added.
"Fiorentina are also one of the most attack-minded teams, so nobody will stop them having any chances."
