Mattia Binotto says the Hungarian GP, a race in which both Ferraris were lapped by Lewis Hamilton, was “very hard to swallow”.
While Hamilton romped to pole position, the race victory and the fastest lap of the grand prix, Ferrari was struggling just to stay inside the top ten.
Vettel, who started fifth on the grid, brought his SF1000 home in sixth place, the first driver lapped by Hamilton.
His team-mate Charles Leclerc lost a late-race tussle against Carlos Sainz to finish outside the points, down in 11th place.
“An extremely disappointing Sunday and the result is very hard to swallow,” said Binotto.
“In qualifying, we had got the most out of the car as it is at the moment, but in the race that was not the case.
“To be lapped is very painful for us and our fans.”
The team boss conceded that Ferrari may need to change its approach to its car philosophy if the Scuderia is to recover lost form.
He added: “Now we return home after this very long trip and we have to try everything we can to improve as much as possible in every area.
“Everyone will have to analyse their work and have the courage to change course if necessary, because the current dynamic is unacceptable.
“There is no other solution to fix this situation.”
— Scuderia Ferrari (@ScuderiaFerrari) July 19, 2020
Such was Leclerc’s lack of pace that the Monégasque believes there must have been “something wrong” with his car.
“To be honest I think there was something wrong in the race,” said Leclerc.
“It just doesn’t match with the car I had in qualifying, but also the day before on Friday, and we haven’t changed much, so we’ll be looking at the data to see what went wrong, because the car was extremely hard to drive on my side today.
“It was a very complicated race. The balance was so much worse than Friday and Saturday, when it was actually better than expected. It just didn’t feel like the same car.
“We need to look further into that to try and understand, as I was struggling a lot.
“There’s lot of work ahead of us.”