Spaniard Sainz accepted Ferrari needed to do a better job but said the mood back home was "a lot better than the news makes it sound".
"When you look back at this last weekend and how many rumours have been around it seems like the place is not in a great moment," he told reporters ahead of Sunday's Saudi Arabian Grand Prix.
"It is so clear to us what we need to improve, how we need to do it and what are the short, medium and long-term targets that I actually am very surprised how some people back at home have been trying to destabilise a bit the team."
Ferrari won two of the first three races last year but Red Bull ended up with 17 victories from 22 rounds - double world champion Max Verstappen (25) claiming 15.
Leclerc, runner-up to Verstappen last season, retired in Bahrain on March 5 with an electronic control unit problem while Sainz finished fourth, bumped off the podium by compatriot Fernando Alonso (41) in an Aston Martin.
One Italian media report last week suggested Leclerc had met Ferrari president John Elkann last week to seek individual assurances.
"This is absolutely untrue," said the Monegasque, who has a 10-place grid penalty for the race in Jeddah due to the control unit having to be switched out.
"There have been loads of rumours around the team which, for once, 90% of them were completely unfounded."
Leclerc said the control unit problem had been understood and should not cause any further concern and the team were united.
"I saw these rumours and then I went to Maranello so at first I was like 'I'm not sure how the team is going to react to it'," he said of the media reports.
"But then we've had a meeting with the whole team, all the Ferrari employees, and I was really surprised. Everybody is fully on it and fully positive still."
Sainz said the high-speed and smooth Jeddah circuit should be better for Ferrari than Bahrain but beating the Red Bulls would still be "extremely difficult".
