The sport's oldest and most successful team, the only ones present since the championship started in 1950, have not won a title since 2008.
They made a strong start this season, with Charles Leclerc (24) winning two of the first three races, but have since suffered a string of strategic errors, driver mistakes and mechanical failures.
Leclerc is second but 109 points behind Red Bull's Max Verstappen with seven races remaining. Team mate Carlos Sainz (28) is fifth and 26 adrift of the Monegasque.
Binotto has been under fire in the media, with some questioning his position but Elkann defended him.
"We have great faith in Mattia Binotto and appreciate everything he and all our engineers have done," he told the Gazzetta dello Sport ahead of Ferrari's home Italian Grand Prix at Monza.
"But there is no doubt that the work in Maranello, in the garage, on the pit wall and at the wheel needs to improve.
"We must continue to make progress and that goes for the mechanics, the engineers, the drivers and obviously, the entire management team, including the team principal.
"Putting our trust in Binotto and his team was the right decision and it has paid off. Thanks to them we are competitive and winning again. But I am not satisfied because I think we can always do better."
Elkann said reliability could be improved and he was optimistic for the future.
"That’s why I believe that before 2026 Ferrari will once again win the constructors’ and drivers’ titles, with Charles Leclerc in pole position," he said.
Elkann is chief executive of the Agnelli family's Exor holding company, which also controls Serie A side Juventus.
The Italian side opened their Champions League campaign this week with a 2-1 defeat at Paris St Germain but Elkann backed coach Massimiliano Allegri to get them winning again.
"Juve is going through a new cycle as has happened many times in the century-old history that links my family to the white and black shirt," he said.
"The team has changed so much, and as a coach Allegri knows the club well and its characteristic spirit of tenacity and strength."
