The Santiago Bernabeu side beat Atletico Madrid 4-1 after extra time in the Champions League final, while recording a 2-1 win over Barcelona in the domestic cup final.
"The team deserves a perfect 10. We have enjoyed a spectacular season. We gave everything out there on the pitch," Di Maria was quoted as saying by Marca.
"We missed out on La Liga, but I think that's partially because our focus was on the Champions League final. I don't know how my team-mates feels about it, but I think we neglected La Liga a bit.
"We won two major trophies in the end, though. It has been a good year. When you look back at this season and analyse it, we won the Copa and the Champions League, so it's been a great year."
Di Maria plays alongside Cristiano Ronaldo at Real Madrid, while teaming up with Lionel Messi at Argentina and he feels privileged to work with two of the best players in the world.
"It is a privilege for me to play with them. One can only feel fortunate. I get along very well with both of them.
"Cristiano has a lot of power and strength, while he also possesses a superb long-range strike. He's been scoring a lot of goals for ages.
"Leo is very quick and great in the one-on-one and even against three or four opponents."