The 24-year-old collected his first title winners' medal last term after performing well as Patrice Evra's understudy at full-back.
Büttner says it's positive for the team to have competition for places and he is hopeful of playing an even bigger part going forward in future United successes.
"The first few months were difficult for me last season. I had to settle in. But I think I did very well. I played 13 games which is good. This season my target is to play more games," the Dutch defender told PA Sport.
"Patrice did very well last season and played some good games. I put pressure on him because I did well when I played. I think Manchester United need that, two good left-backs. I want to go for the left-back position. That is my target, to play many games.
"Everyone wants more medals. Next season I want one again," he added.
"My [title] medal is at home in Holland. Everyone wanted to see it. I have started to build a new house and something like that will have a special place. It was unbelievable to win a medal in my first season at Manchester United, but I want more.
"We want to win every game. We want to be champions again and we have a very good team in order to do that."