Former England defender Cole signed a two-year deal with the Serie A club earlier this month following his release by Chelsea at the end of last season.
He urged more English players to step out of their ‘comfort zone’ and go overseas as he was presented to the media, and insists he is driven by a desire for trophies.
Roma finished second in the league last term, 17 points behind champions Juventus, but Cole believes they can challenge for the title.
“Our aim is winning. Not doing it would be a disappointment,” Cole told the Roma Channel prior to the club’s tour of America.
“We have a team able to win the Italian league."
Cole had the opportunity to play Major League Soccer but believes it was the right decision to stay in European football.
“I chose to come here for the ambitions of this club,” he said.
“I've spoken with coach Rudi Garcia and he showed me this winning will.
“I have had other offers from USA, but I didn't want to sit on the beach yet.
“I won a lot in my career and I have no intention to stop. I'm here to win.”