After Verstappen and Kvyat swapped seats, prospects for the demoted Toro Rosso driver looked bleak over the summer as he had to contend with a better performing Carlos Sainz at the Faenza-based out.
But Kvyat kept his head down and gradually improved his relative performance. Holding Verstappen at bay in Singapore for almost half of the race, and his subsequent ninth place finish, went a long way towards convincing Red Bull to keep the Russian for 2017.
"I think that it was generally positive to show that he still has the speed and the car control to fight against Max and also leave him behind," Tost told Motorsport.com.
"For his self-confidence it was very important. The big turnaround was done in Singapore where he really showed a good race and qualifying as well.
"And also afterwards he showed good performance. Therefore for me it was clear that he should continue with us."
Tost readily admits that Kvyat's bumpy ride in 2016 would have rocked any driver's psych.
"After changing from Red Bull Racing to Toro Rosso, it was a hard time for him. Naturally you also get a little bit weak from the confidence side.
"So it's a positive influence and impact if you can keep a driver like Max Verstappen behind you with a Toro Rosso car. The most important part for race driver that he is clear in his head and that he is self confident."
Tost is expecting Kvyat to return once again to his full potential in this year.
"In sports in general, you have ups and downs. But if a driver or a sportsman in general shows that he can win races and championships, then you know he has in mind all the ingredients he needs to become successful and to be successful.
"Therefore I'm convinced that Daniil is coming back, that he will become successful and I expect a very strong season from him in 2017."