"He is our leader but he wanted the limelight to be on these guys - the guys that did it out on the water," said the billionaire technology tycoon.
"In my opinion Russell should be up here, he is our leader. He described himself as a facilitator - well, what a facilitator."
Ellison said Coutts had played a key role in plotting the downfall of the Kiwi team that had looked unstoppable in the early stages of the regatta.
He said were it not for the perseverance of the 51-year-old, who has not sailed in an America's Cup for more than a decade, Oracle might not have unlocked the code to the extra boat speed needed to beat Team New Zealand.
"He asked a lot of hard questions and came up with a lot of important answers," said Ellison.
"He wasn't out on the water, but a lot of his ideas and a lot of strategies and techniques we used to mode that boat and speed it up came from Russell Coutts."
Oracle skipper Jimmy Spithill said having an experienced sailor like Coutts watching from off the boat and seeing things the crew weren't seeing helped them develop at the speed they did. "To have their thoughts looking from the outside in, was great. A lot of the guys on board the boat you can't get that big picture."
Coutts absence from the post-race celebrations has heightened speculation that he may be headed to another syndicate in the next Cup cycle. Ellison said he would like to see Coutts stick around. "Russell Coutts has never lost an America's Cup - not a bad record. So as long as Russell wants his job we're blessed to have him."