Robben, 23, who has penned a five-year deal at Real, said: "In the early stages, yes they could have done more.
"And when a massive club like Real Madrid shows an interest it makes it easy and gives you a great feeling.
"When you compare the feeling of confidence you get from Real and Chelsea then you have to go where you feel you will be most happy and that's what I did."
Robben's dad and agent Hans backed his son by insisting Chelsea made no attempt to try to keep him.
Hans said: "We thought it was the intention of Chelsea for Arjen to stay but they never offered a new contract.