Leclerc has only recently solved qualifying issues, which included a crash on the Saturday of the Azerbaijan GP, while Vettel spun out of contention in Bahrain and then had victory in Canada taken away from him by the stewards as correcting an off-track moment put him in the path of Lewis Hamilton.
The Silver Arrows' dominant winning start to 2019 was only stopped last time out in Austria by Max Verstappen and Red Bull.
And Binotto says more risky driving might be needed if the Scuderia are to get into the winners' column this year.
"It certainly is not easy for him, no question," Binotto told Auto Bild of the mounting pressure on Vettel.
"He has this dream to become World Champion with Ferrari and we support him to realize this dream.
"He understands his role in rebuilding the team. He is very important to me, because he has a lot of experience and because he has expertise and great skills.
"On the one hand he is a team player, on the other hand a leader who has great enthusiasm at work.
"He also enjoys his job if he does not win, which is not so easy. But he knows that this enthusiasm is a key to winning in the future. And he also knows: nobody can win alone, we can only do it all together. The team is the basis."
Of Vettel's errors, Binotto explained: "It was always racing situations where Sebastian was at the absolute limit - sometimes over it as well.
"Our drivers have to drive even more risky right now to keep up. In Canada, for example, it was not easy for Seb to stay ahead of Hamilton, who probably had the faster car.
"The future is always more important than the past. What is important is that he feels that we trust in him and build on him. And we do."
GPFans is a multi-platform, multi-language brand dedicated to Formula One coverage. We bring you all the ins and outs of the sport, 24/7, everything from up-to-the-minute news and features to the latest viral stories and clips.
We believe that a new generation of exciting, outspoken drivers will make F1 more popular than ever before, and we want to give our users access to as much of their heroes as possible, on and off the track. From Lewis Hamilton to Max Verstappen, Daniel Ricciardo to Sebastian Vettel, we provide in-depth analysis of every every Grand Prix in the season, from Australia to Abu Dhabi.
With Formula One under the new ownership of Liberty Media, how the sport is being covered is evolving, and GPFans will look to be at the heart of this progression into new media, as one of the fastest-growing sites covering the king of motorsports.