After a shaky start, United now sit fourth in the table, eight points adrift of leaders Chelsea, and the Brazilian believes the team are improving by the week as they adapt to Louis van Gaal's tactical philosophy.
Speaking to Sky Sports News HQ he said: "In my opinion, something changed. We have new players in the squad. Manchester United signed a lot of players and we have a new manager as well.
"Season after season, things change and for us especially this year. All the coaching staff is new, and we have new team colleagues. Van Gaal always relies on his philosophy and now we are starting to understand this.
"I worked with Sir Alex Ferguson and other managers. Van Gaal is a strong coach who admires the right things. He asks for everyone to be on time for the activities; we can't be late.
"He likes to see us training hard. He has some differences, especially the philosophy, so we have to adapt to this. However, it is something right and the proof is the titles he has won.
"Everything takes time but if we start to understand the way of playing like we are doing and the results are positive and everything starts to run smoothly, then for sure we have the chance to win the title.
"We have three difficult games against West Brom away, after this we face Chelsea, and then Manchester City in their stadium. These games will be very important for us."
Rafael has been impressed with the impact Argentina international Angel di Maria has made since joining the club from Real Madrid for a British record fee of £59.7million.
He said: "Everything changes when another player sees di Maria in your team. I wouldn't say it was a relief but it's always good to see him playing because he can decide a match in one play and he is doing this. He has three goals and three assists it's important for the team to see players of this calibre."