After finally getting his work permit, the innovative German took charge of the team for the first time, replacing Ole Gunnar Solskjaer sacked at the helm of Old Trafford after Michael Carrick temporarily took over.
Fred settled the scores for United with a stunning right-footed winner midway through the second half.
Rangnick gave those who won a comeback victory over Arsenal a first audition under his leadership and the 63-year-old caretaker was rewarded with three Premier League points and a rare clean sheet.
According to Palace Vieira manager, however, a draw would have been a fairer result.
In his post-match press conference, the Palace manager highlighted a key moment that went against him and assessed the impact Rangnick could have on United after stepping into the hot seat.
Vieira said: “I thought the game would end in a draw. Neither team created too many chances. When we had this chance with Jordan [Ayew] we didn’t take it. Against the big teams, you are punished.
“In these games you have to score them.
“He’s a team player and does a fantastic job outside of possession, but forwards are judged by the goals they score. I’m really disappointed because he deserved to score. “
Vieira added: “I think we weren’t brave enough to play at the back. We were missing players, there was a lack of confidence in possession. We did not allow ourselves to play.
Do you agree with Vieira? Give your opinion in the comments section below.
“With the new manager, we didn’t know how they were going to play. But we prepared with our form. When you look at their odds, I think a draw would have been a fair result.
“It’s important to win football matches, but at the same time, you have to look at the performances. We are very close. We have to take it on the chin and keep working. “
Sign up for our United newsletter to never miss an Old Trafford update this sraison.