The five-time world player of the year has called for a change of mindset within the Old Trafford dressing room to ensure United turn around their recent poor form.
Ronaldo has also backed Ralf Rangnick to lift the club but it admits it will take time for the interim manager’s methods to take hold.
United are currently seventh in the table after defeat by Wolves in their last outing.
Ronaldo told Sky Sports: “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.”
Rangnick was brought in until the end of the season after the sacking of Ole Gunnar Solskjaer following a poor run of results in November.
The German has steadied things to a degree but the team’s style of football has still attracted criticism and there have been reports of disquiet within the squad.
Ronaldo said: “He arrived here five weeks ago. 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.”