The Canaries have won three of their first four games of the season, including a 1-0 win over Ipswich Town in the East Anglia derby earlier today, which left them third in the table.
Adams told Sky Sports News: "I know there were some doubts when I got the job, but it is all about results.
"We are a Premier League club, we should be in the Premier League. We don't have to sell any players, only if someone offers the right price, and I am delighted with the five players we have brought in.
"I have played in East Anglian derbies and it means just as much to win as a manager. It is not an easy place to go but I and the players knew exactly what it meant to our supporters."
Norwich will play Bournemouth next weekend, with the Cherries having lost their last two matches.