But rumblings that all was not well in the Murray camp came to light following the Briton's decision to appoint twice grand slam champion Amelie Mauresmo as head coach last June.
It led to Venezuelan Vallverdu and Green to snap ties with Murray in November.
"The most important point in any team is that everyone has the same vision, everyone wants to move forward together," Murray told The Independent in Perth, where he is fine-tuning his preparations for this month's Australian Open.
"I feel that's what I have now. Maybe the last four or five months of last year it wasn't like that. It's not as much fun travelling when that's the case. If everyone isn't right into it, that isn't how you want to work."
Asked if Vallverdu thought he should have been promoted to the top job following the departure of Murray's former head coach Ivan Lendl last March, the world number six replied: "That's possible.
"(But) if you look at last year I spent only one tournament... with Ivan, at the Australian Open. The rest of the time I was with Dani every single week. I didn't have another coach travel with me at all.
"So he was the coach responsible for my training and all my practices at all of the tournaments. Maybe it didn't go as well as either of us would have liked and that's why I felt like I needed someone else."
While Murray was frustrated at his inability to reach a grand slam final for the first time in five years in 2014, Vallverdu was promptly hired by former Wimbledon finalist Tomas Berdych.
"For him to get the opportunity to work with someone like Berdych is fantastic. He's obviously a top player and it will be a good challenge for him," added the 2013 Wimbledon champion.
Murray, who has now fully recovered from the back surgery that hampered him during the early part of last season, has also been working with a sports psychologist in the hope of returning to the grand slam winner's circle.
"I think when it comes to psychology it has to be something that the player wants and the player buys into," Murray said.
"When it's someone else's suggestion in the past I haven't felt like it's worked. But just now I think it's working well."
(Reporting By Michael Hann in London, editing by Pritha Sarkar)
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