"I experienced the same sort of difficult times when I was at McLaren with Mika [Hakkinen]," Coulthard told Ilta Sanomat.
"Valtteri just needs to work hard, find out where the gap to Lewis is and believe that he will be able to close it."
"Valtteri is a quick and talented driver. As a person he is quiet and reserved, but he needs to think about his races and everything that brought him to this point and believe in himself.
"At the same time we also have to realise that he has one of the fastest ever drivers as his teammate."
The championship continues with the United States Grand Prix on Sunday.