The young Russian driver moved to Red Bull to replace Sebastian Vettel; following a debut season at Toro Rosso where he became the youngest driver in the history of Formula One to score points.
Kvyat said: "You just have to keep working hard, put it all together and hopefully it brings some good things in the future.
"Last year when they (Toro Rosso) signed me to F1 there were a lot of stupid talks going on and I really wanted to show good pace straight away and I think I managed that.
"So now I can focus on the right things at Red Bull and that helps a lot as last year went good and now I am just focused on bringing the best result possible."
He added: "Every driver in F1 is different. I will keep doing what I have been doing in the past, there will be a few tweaks as you have to get used to the team and adapt yourself to it."