The Brazilian midfielder completed his loan switch to Fiorentina in January, a move he hopes to make permanent if he impresses.
And while he wishes David Moyes and United every success in the future, Anderson thinks his time at Old Trafford was hindered by a lack of opportunities that didn't allow him to play his best football.
"To be honest I've not had the chance," Anderson told The Sun. "He gave me one chance or a half but not a lot.
"He is the manager and I have to respect him. He treated me well and he has a lot of players. I have to play and have my chance. It is better for me at Fiorentina.
"The manager wants me and has shown his trust, I can show him my football. Even though the contract is only on loan, I want to stay for a long time."
After reports earlier in the week seemed to suggest Anderson was one of several unhappy players at Old Trafford under Moyes, the former-Porto star also wanted to take the opportunity to put those rumours to bed.
"At United the fans love me and I like the club so much. Sometimes football changes and you have to change. It will improve me as well.
"There is a big opportunity to go to the Champions League, I've been very impressed here.
"Manchester United changes all the time. Even with Alex Ferguson there were changes. I hope they can succeed this season and overcome this period."
Manchester United have struggled to find the right balance in midfield, with Ryan Giggs, Tom Cleverley, Phil Jones, Michael Carrick and Marouane Fellaini used in various combinations.
The Old Trafford club currently sit seventh in the Premier League and face a real battle to qualify for the Champions League next season.
They remain in this year's competition and face Olympiakos in the last-16 this month.