Baker, who has spent the past two seasons on loan with the Eredivisie side, scored twice in the Dutch Cup semi-final before playing in the final against AZ Alkmaar who Vitesse went on to beat 2-0 to claim their first piece of silverware in their 125-year history.
Speaking to Goal, the 22-year-old said: "Overall I think Chelsea are happy with what I did [on loan].
"There's still aspects of my game that I could carry on working on. I need to keep working day-in-day-out. The past two years that I have been away on loan have been fantastic.
"The achievements I have made have been unforgettable but we need to just carry on now and keep going as far as possible in my career. My family are just as cheerful as me. They were at all my games; they were there in the final so they come every step with me.
"Moving from playing as a kid to now, I am grateful for the people that I have around me. I had a lot of messages after the game, former coaches from Chelsea came to watch. People from the academy too, so it was something that I will never forget.
"The first year [away from Chelsea at Vitesse] was more learning, adapting to living away, adapting to a different league. The second year was more producing and showing what I am capable of. I think it has been fantastic to move away and learn different things but I want to be back in England."
When then asked about his future, Baker said: "For me, the two years away were fantastic and I am always open to suggestions to see who comes in but it would be great for me to play more in England.
"Chelsea have got into the Champions League again so they are going to need to get players into their squad. There are going to be a lot of games. I just want to carry on playing football as much as possible. I love playing, I want to do it as much as I can."