The 1-0 win over Shakhtar Donetsk came courtesy of Phil Jones' second-half strike ensured David Moyes' side topped Group A and avoided a third successive home defeat for the first time since 1962.
United have not won in the Premier League since November 10 when they beat leaders Arsenal at Old Trafford but they head to Villa Park on Sunday looking to get their season back on track.
"We are the players and if we lose we have to look to ourselves but I think we did well against Shakhtar," the Dutch left-back said.
"It is hard for everyone when we don't win at home. That is why we fought for every ball and you could see everyone doing that.
"It was good for the team and after recent games to win is good for confidence. It was a very important win.
"We have been a bit unlucky in the league but we have done well in the Champions League and hopefully we can go on a run in the league and beat Villa in the next game."
Buttner was deputising for the injured Patrice Evra against the Ukrainian club but after only 20 minutes of football since the end of October he started to struggle late on and was eventually replaced by Antonio Valencia.
Moyes said Evra's injury was not too serious so the Frenchman may well come back for the Villa game but Buttner is ready to take his chance should the opportunity arise.
"I had cramp in my calf because I've not played for a long time, that was my first game in a month and the last few minutes I was tired," he added.
"I am okay for the weekend. I don't know whether Patrice's injury is bad.
"It is nice to play more games and I hope I can play but I have to wait as it will be the choice of the manager."
Striker Wayne Rooney, captain for the night, admitted victory was the only acceptable outcome after their recent struggles.
"The most important thing was to get back to winning ways and top the group so we've done that," he told uefa.com.
"It could have been better at times but thankfully we got the win. (It was) win at all costs - after the last two games we knew it was vital.
"We got a good result and if you'd have said beforehand that we'd win the game after the last two results, we'd have certainly taken that.
"The campaign has been good this year in Europe so we just have to try and get that consistency in all our games, whether it is Europe or the Premier League.
"Hopefully we can do that in the upcoming games and get back in a good position."