The Scuderia finished second in the drivers and constructors championships last time out after an error-strewn campaign, way behind Red Bull whose top driver Verstappen comfortably retained his title.
"The goal is to win, clearly," said driver Charles Leclerc, who took the SF-23 for a spin around the Maranello track in front of some of the team's passionate supporters.
"The feeling of winning is what motivates me, motivates all the team too. I'm really looking forward to getting back in the car and trying to win the championship."
The coming season is the first for team principal Frederic Vasseur, who took charge in December following the resignation of Mattia Binotto the month before.
Binotto was considered culpable for last season's frequent missteps, including pitlane errors and reliability issues which damaged Leclerc's attempt to keep up with Verstappen.
Ferrari began with two wins in the opening three Grands Prix but were then swept aside by Red Bull and Verstappen, who won the drivers title with three races remaining and eventually finished 146 points ahead of Leclerc.
The new car is designed with the aim of improving aerodynamics and the reliability of the engine, the latter being one of the key problems last time out.
"You can feel the responsibility for the team, it's a great honour but at the end of the day the important thing is to be successful," said Frenchman Vasseur.
"We want to deliver and I don't want to be happy just because I'm at Ferrari, the most important is to win.
"Last year is not a secret, it was not the best aspect with the engine, we've done a good job and we're ready for the season."