The next race is next Sunday, also on home soil at their own Mugello circuit where they are supposed to celebrate the team's 1,000th race.
"This is a very difficult moment for the whole team and as part of it, I am suffering along with everyone else," said Vettel, who was racing for the last time at Monza as a Ferrari driver. He is leaving at the end of the year.
"But this is our reality right now and we need to try and do the best we can, to have a worthwhile final part of the season with still plenty of races to go. We have a lot of work to do and we have to be focused on that."
Team boss Mattia Binotto said the double retirement was "the worst possible end to a very difficult weekend".
"After Belgium, we knew here, too, we would struggle a lot, and so it turned out. That was clear in yesterday’s qualifying, but failing to get either car to the chequered flag really hurts," he said.
"It’s even more disappointing that Sebastian’s retirement was down to a lack of reliability on the car. Problems like that, in this case with the brake system, should not happen."
Ferrari feels the pain after yet another diabolical race weekend
Image: Mark Thompson/Getty Images
Ferrari suffered their worst Italian Grand Prix in decades on Sunday, and it hurt.
Charles Leclerc, last year's winner in front of an army of passionate fans, crashed out heavily at Parabolica after 23 laps while Sebastian Vettel careered off on lap six with a brake failure.
The last time Formula One's oldest and most glamorous team had a double retirement in their home race was in 1995, but then at least Gerhard Berger managed to rev up the crowd by qualifying third.
This time, in a race without spectators due to Covid-19, neither Ferrari started in the top 10.
Hamilton posts fastest lap in F1 history to take pole at Monza
The next race is next Sunday, also on home soil at their own Mugello circuit where they are supposed to celebrate the team's 1,000th race.
"This is a very difficult moment for the whole team and as part of it, I am suffering along with everyone else," said Vettel, who was racing for the last time at Monza as a Ferrari driver. He is leaving at the end of the year.
"But this is our reality right now and we need to try and do the best we can, to have a worthwhile final part of the season with still plenty of races to go. We have a lot of work to do and we have to be focused on that."
Team boss Mattia Binotto said the double retirement was "the worst possible end to a very difficult weekend".
"After Belgium, we knew here, too, we would struggle a lot, and so it turned out. That was clear in yesterday’s qualifying, but failing to get either car to the chequered flag really hurts," he said.
"It’s even more disappointing that Sebastian’s retirement was down to a lack of reliability on the car. Problems like that, in this case with the brake system, should not happen."
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