Man Utd are currently on a run of just one defeat in ten matches, with most of those presided over by Rangnick.
He, though, has come under fire for some very poor performances and what often appears to be questionable attitudes from his team on the pitch.
Ronaldo, though, has pleaded for patience and insists Rangnick is definitely improving the Red Devils.
"He arrived here five weeks ago," Ronaldo said of Rangnick. "He changed many things but he needs time to put his ideas through the players and on the pitch.
"It takes time but I believe that he is going to do a good job. We know we don't play the best football, as we should do, but we have many games to improve.
"Since he arrived I think in some points we are better, but he needs time."
However, despite asking for time, Ronaldo also said that even fourth place in the Premier League should be considered unacceptable for United.
"Manchester United should win the league or be second or third. I don't see any other position for Manchester United.
"In my heart, I don't accept that our mentality be less than being in the top three in the Premier League, in my opinion.
"I think to build up good things sometimes you have to destroy a few things. New year, new life, I hope that Manchester can be at the level people want, especially the fans. We are capable of changing things now.
"We can do it better, all of us. I don't want to be here in the club to fight to be in sixth or seventh place. I am here to try to win, to compete. I believe if we change our mind we can achieve big things."