The Red Bull-owned team has been plagued by issues so far with its STR9, as have all of the Renault-powered squads.
But with four days of testing in Bahrain still to come, its drivers believe that the situation is bound to improve.
"Of course we need to keep calm," said Vergne. "It's pretty easy, because the first race is not here yet.
"I think there are enough other people getting stressed, so I keep positive.
"We have good people, and with Renault I believe they have the best people to fix it so I'm sure we will have something good really soon."
Light at the end of the tunnel for Renault
Russian rookie Kvyat added: "We shouldn't panic and I know that we will not. It should all be OK.
"I can't say a particular day or race where we are going to be good enough, we just have to work hard.
"We are in the catch-up phase but I am pretty sure we are going to make it."
Vergne added that he was buoyed by the feeling of the Toro Rosso, and he believes that the team's pace is stronger than it has looked in testing so far.
"[In Bahrain last week] I did two good laps when the car was working but I had to pit because of red flags," he said.
"They would have been really good lap times considering our lack of running, and comparing to our direct competitors it was looking really good.
"So we need to take this into account, and we have to stay positive.
"The first race is not here yet and there is still four days to come. I have big faith in all the people working hard to fix things at the moment."