The 23-year-old was a regular fixture at right-back under David Moyes, but was unable to prevent United from missing out on European football as they finished seventh in their worst campaign since the 1989/90 season.
A hamstring injury picked up in late March saw Rafael miss the remainder of the season as Moyes was sacked and replaced by Ryan Giggs for the final four league games.
Rafael admitted that it was difficult to adapt following Sir Alex Ferguson's departure last summer, but believes that he and his team-mates should take responsibility for United's failings.
"The year was not normal. I had been there for six years, I was a champion three times, runners-up twice," he told Globo Esporte
"I think this is football, we changed manager after 26 years and that affects any team. Each manager has his own style.
"The players are to blame too, the things changed off the field, now we have to try again next season."
Holland boss Louis van Gaal has since been appointed as Moyes' successor on a three-year deal and he will take charge at United as soon as his side's World Cup campaign is over.
According to Rafael, the 62-year-old comes with glowing reports from his United team-mate and Dutch captain Robin van Persie.
"Van Persie said many good things about him especially when his name was being linked to the club," he said.
"I heard a lot when he was at Barcelona and Bayern too. Now we have to wait."
Rafael has two caps for Brazil but says that missing out on Luiz Felipe Scolari's World Cup squad came as no surprise having failed to feature internationally for almost two years.
"After I wasn't called up last year when I was playing well, I felt it would be hard to be called up for the World Cup," he admitted.