The Formula Renault 3.5 championship leader had been heavily linked with the seat, often seen as a stepping stone for drivers on the Red Bull development programme.
However, Sainz Jr was overlooked in favour of the 16-year-old Dutchman, who is only in his first season in single-seater racing, and the Spaniard struggled to contain his surprise at the decision.
He told Crash.net: "It was a shock. I just need to focus on myself and win the championship to prove to all the people who think I am not good enough, that I can be the first Red Bull junior to win the championship and youngest ever too.
"It was a big surprise for me. It was unexpected, especially when you are leading a championship but these things happen.
"I would not be in this championship if was not for Red Bull so I am thankful for that. It is a tricky situation."
Verstappen will partner Daniil Kvyat when he becomes F1's youngest driver in history next season.