The 25-year-old scored a first-half brace for the Rams which proved to be enough to secure the three points in their Championship encounter.
Butterfield believes that his side's work ethic at the back in the second half was vital to claim the three points over their promotion rivals, continuing their good run of form following their victory against Cardiff City last week.
He told the club's official website: "It's a massive win. We identified these first four games after the last international break as big games for us. We have played two of the teams and won two so we are all delighted. This is a tough place to come to. Hull are clearly a good team and are probably the best that we have played this season.
"It was tough, but we got the two goals, showed how well we can defend and put in a real shift to come out with the win. In most of the games this season we have dominated with the ball and shown what a good passing side we are.
"When you come up against one of the best teams in the league you are not going to get it all your own way. You have to be able to defend, work hard and put a shift in. We have shown in different games and this one especially that we can do different things as a team. We are showing all of the qualities that we have got, with and without the ball. Our performance had a bit of everything."
Derby moved above Hull to claim top spot in the Championship as a result of their win.