Ferrari team boss Mattia Binotto says they "cannot accept" another year as poor as 2020.
Ferrari were sixth in the constructors' championship with a best result of second place. It was their worst season since 1980, when they finished 10th.
Binotto said: "It has been a very hard season, even harder than we expected."
But he said he believed the team could improve in 2021, saying: "Third is not impossible and that should be our minimum objective for next season."
He admitted, though, that "finishing third [in the constructors' championship] will not be an easy job" and said he expected both Racing Point and McLaren to be strong.
And he said Ferrari had no hope of catching Mercedes in 2021: "The gap to the best team is very high and we will not close it next year."
Ferrari's biggest issue in 2020 was a lack of engine performance after a series of rule clarifications and a confidential settlement last winter with governing body the FIA, which believed but could not prove that the engine was not being run legally at all times in 2019. Ferrari denies any wrongdoing.
Binotto, who was talking in an end-of-season news conference, admitted Ferrari had the worst engine on the grid in 2020 but said the team had made progress with a new engine design for next season.
"The engine is running well on the dyno [test bed]," Binotto said. "In terms of performance, it has progressed well. Luckily we can have a completely new power-unit, otherwise we would be at a disadvantage.
"I think we will be back to be competitive as a power unit; we will not be the lowest in the field. That is the feeling I have got."
Development on cars is limited for 2021 because of cost-saving changes agreed as a result of the coronavirus pandemic, but Binotto said he believed Ferrari could make a step forward.
However, he said that developing a new car for 2022, when a major set of rule changes that significantly change the cars will come into force, was "more important than 2021, as we are starting a new competitive era and if you start behind it will be difficult to catch up".
Binotto said he felt "fully supported" by chairman John Elkann and vice-president Piero Ferrari, but added: "I know my time [as team principal] is not infinite. I am aware that as a team we need to do well in the next seasons… [but] it will take some time."
Introductions for Sainz
Sainz (right) finished sixth in the 2020 drivers' championship for McLaren
New driver signing Carlos Sainz, a replacement for Sebastian Vettel as Charles Leclerc's team-mate, had his first day at the team's Maranello factory on Friday.
Sainz, who joins from McLaren, said: "It is a special day for me and one I will probably never forget."
Sainz has signed a two-year contract, while Leclerc is committed to Ferrari until the end of 2024 and the team have made it clear the 23-year-old from Monaco is the main hope for success.
Leclerc scored 75% of Ferrari's points in 2020 as he comfortably out-performed four-time champion Vettel in a difficult car.
Binotto said: "Charles had a great season. He is very talented and very fast. He has developed as a person and as a leader and today all the engineers see him as an important reference point in the future."
But Binotto said there would be no favouritism towards Leclerc at the start of next season.
"There is nothing in the contract of Charles [about] him being the leader. They will be free to fight on track," Binotto said.
"It is important they will not damage themselves. They will have equal opportunities at the start of the season.
"The top priority is to maximise the team points and it may be that in some races the two are accepting decisions to optimise the team's interests but by doing the team interest we are helping the driver interest.
"And later in the season if one has a clear advantage and one can achieve something the other can't, it will be an open discussion [about team orders]."
Asked what he expected of Sainz, Binotto said: "I expect him to contribute to the constructors' championship. It is important to have two drivers doing very well in the car.
"By doing well in the constructors' championship, it means the two drivers are doing well in the drivers' classification. I am hoping and pretty sure that Carlos will help us in terms of doing better in terms of constructors.
"I am expecting him to be a great team-mate and I am expecting he is a hard worker. He is a leader and I expect him to help develop the team in the future."
-- Courtesy of BBC Sport